Kodaka, Kazunori Equivalence bundles over a finite group and strong Morita equivalence for unital inclusions of unital \(C^*\)-algebras. (English) Zbl 07655819 Math. Bohem. 147, No. 4, 435-460 (2022). MSC: 46L05 46L08 PDF BibTeX XML Cite \textit{K. Kodaka}, Math. Bohem. 147, No. 4, 435--460 (2022; Zbl 07655819) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori Strong Morita equivalence for completely positive linear maps on \(C^\ast\)-algebras. (English) Zbl 07648479 Bull. Iran. Math. Soc. 48, No. 6, 3743-3765 (2022). MSC: 46L05 46L07 PDF BibTeX XML Cite \textit{K. Kodaka}, Bull. Iran. Math. Soc. 48, No. 6, 3743--3765 (2022; Zbl 07648479) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori The Picard groups of inclusions of \(C^*\)-algebras induced by equivalence bimodules. (English) Zbl 1504.46066 Can. Math. Bull. 65, No. 3, 743-758 (2022). MSC: 46L05 46L08 PDF BibTeX XML Cite \textit{K. Kodaka}, Can. Math. Bull. 65, No. 3, 743--758 (2022; Zbl 1504.46066) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori Strong Morita equivalence for conditional expectations. (English) Zbl 1495.46042 Proc. Edinb. Math. Soc., II. Ser. 65, No. 1, 182-213 (2022). MSC: 46L05 PDF BibTeX XML Cite \textit{K. Kodaka}, Proc. Edinb. Math. Soc., II. Ser. 65, No. 1, 182--213 (2022; Zbl 1495.46042) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori Strong Morita equivalence for inclusions of \(C^*\)-algebras induced by twisted actions of a countable discrete group. (English) Zbl 1486.46073 Math. Scand. 127, No. 2, 317-336 (2021). Reviewer: Evgenios Kakariadis (Newcastle upon Tyne) MSC: 46L55 46L05 PDF BibTeX XML Cite \textit{K. Kodaka}, Math. Scand. 127, No. 2, 317--336 (2021; Zbl 1486.46073) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori; Teruya, Tamotsu Coactions of a finite-dimensional \(C^*\)-Hopf algebra on unital \(C^*\)-algebras, unital inclusions of unital \(C^*\)-algebras and strong Morita equivalence. (English) Zbl 1466.46045 Stud. Math. 256, No. 2, 169-185 (2021). MSC: 46L05 46L08 PDF BibTeX XML Cite \textit{K. Kodaka} and \textit{T. Teruya}, Stud. Math. 256, No. 2, 169--185 (2021; Zbl 1466.46045) Full Text: DOI arXiv OpenURL
Pal, Pavel; Gupta, Sugato; Mukherjee, Rajlaxmi; Sardar, Sujit Kumar Isomorphisms of some lattices obtained from Morita context of semigroups using fuzzy notions. (English) Zbl 1474.20109 Southeast Asian Bull. Math. 44, No. 5, 703-718 (2020). MSC: 20M10 20N25 20M30 20M50 16D90 PDF BibTeX XML Cite \textit{P. Pal} et al., Southeast Asian Bull. Math. 44, No. 5, 703--718 (2020; Zbl 1474.20109) OpenURL
Kodaka, Kazunori The generalized Picard groups for finite dimensional \(C^*\)-Hopf algebra coactions on unital \(C^*\)-algebras. (English) Zbl 1443.46044 Turk. J. Math. 43, No. 5, 2511-2539 (2019). MSC: 46L55 46L05 16T05 PDF BibTeX XML Cite \textit{K. Kodaka}, Turk. J. Math. 43, No. 5, 2511--2539 (2019; Zbl 1443.46044) Full Text: arXiv Link OpenURL
Laan, Valdis; Reimaa, Ülo Morita equivalence of factorizable semigroups. (English) Zbl 07079853 Int. J. Algebra Comput. 29, No. 4, 723-741 (2019). MSC: 20M30 20M50 PDF BibTeX XML Cite \textit{V. Laan} and \textit{Ü. Reimaa}, Int. J. Algebra Comput. 29, No. 4, 723--741 (2019; Zbl 07079853) Full Text: DOI OpenURL
Ng, Chi-Keung; Wong, Ngai-Ching On the decomposition into discrete, type II and type III \(C^*\)-algebras. (English) Zbl 1411.46043 Math. Proc. Camb. Philos. Soc. 165, No. 3, 475-509 (2018). MSC: 46L05 46L45 PDF BibTeX XML Cite \textit{C.-K. Ng} and \textit{N.-C. Wong}, Math. Proc. Camb. Philos. Soc. 165, No. 3, 475--509 (2018; Zbl 1411.46043) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori; Teruya, Tamotsu The strong Morita equivalence for inclusions of \(C^{\ast}\)-algebras and conditional expectations for equivalence bimodules. (English) Zbl 1402.46039 J. Aust. Math. Soc. 105, No. 1, 103-144 (2018). Reviewer: Maryam Amyari (Mashhad) MSC: 46L05 PDF BibTeX XML Cite \textit{K. Kodaka} and \textit{T. Teruya}, J. Aust. Math. Soc. 105, No. 1, 103--144 (2018; Zbl 1402.46039) Full Text: DOI arXiv OpenURL
Laan, Valdis; Márki, László; Reimaa, Ülo Morita equivalence of semigroups revisited: firm semigroups. (English) Zbl 1435.20075 J. Algebra 505, 247-270 (2018). Reviewer: Chen Yuqun (Guangzhou) MSC: 20M30 20M50 16D90 PDF BibTeX XML Cite \textit{V. Laan} et al., J. Algebra 505, 247--270 (2018; Zbl 1435.20075) Full Text: DOI Link OpenURL
Kodaka, Kazunori Equivariant Picard groups of \(C^\ast\)-algebras with finite dimensional \(C^\ast\)-Hopf algebra coactions. (English) Zbl 1387.46044 Rocky Mt. J. Math. 47, No. 5, 1565-1615 (2017). MSC: 46L05 46L08 PDF BibTeX XML Cite \textit{K. Kodaka}, Rocky Mt. J. Math. 47, No. 5, 1565--1615 (2017; Zbl 1387.46044) Full Text: DOI arXiv Euclid OpenURL
Amini, Massoud \(C^\ast\)-algebras of 2-groupoids. (English) Zbl 1346.18007 Rocky Mt. J. Math. 46, No. 3, 693-728 (2016). Reviewer: Chris Heunen (Edinburgh) MSC: 18D05 PDF BibTeX XML Cite \textit{M. Amini}, Rocky Mt. J. Math. 46, No. 3, 693--728 (2016; Zbl 1346.18007) Full Text: DOI Euclid OpenURL
Akemann, Charles A.; Amini, Massoud; Asadi, Mohammad B. Which multiplier algebras are \(W^*\)-algebras? (English) Zbl 1424.46082 J. Oper. Theory 74, No. 1, 125-132 (2015). MSC: 46L10 47L30 46L08 PDF BibTeX XML Cite \textit{C. A. Akemann} et al., J. Oper. Theory 74, No. 1, 125--132 (2015; Zbl 1424.46082) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori; Teruya, Tamotsu The strong Morita equivalence for coactions of a finite-dimensional \(C^*\)-Hopf algebra on unital \(C^*\)-algebras. (English) Zbl 1351.46054 Stud. Math. 228, No. 3, 259-294 (2015). MSC: 46L05 46L08 46L55 PDF BibTeX XML Cite \textit{K. Kodaka} and \textit{T. Teruya}, Stud. Math. 228, No. 3, 259--294 (2015; Zbl 1351.46054) Full Text: DOI OpenURL
De Commer, Kenny; Yamashita, Makoto Tannaka-Kreĭn duality for compact quantum homogeneous spaces. II: Classification of quantum homogeneous spaces for quantum \(\mathrm{SU}(2)\). (English) Zbl 1334.46050 J. Reine Angew. Math. 708, 143-171 (2015). Reviewer: Marta Macho Stadler (Leioa) MSC: 46L65 46L87 PDF BibTeX XML Cite \textit{K. De Commer} and \textit{M. Yamashita}, J. Reine Angew. Math. 708, 143--171 (2015; Zbl 1334.46050) Full Text: DOI arXiv OpenURL
Hirota, Yuji Equivalence of the categories of modules over Lie algebroids. (English) Zbl 1318.53092 J. Symplectic Geom. 13, No. 2, 387-419 (2015). Reviewer: Angela Gammella-Mathieu (Metz) MSC: 53D17 53D15 PDF BibTeX XML Cite \textit{Y. Hirota}, J. Symplectic Geom. 13, No. 2, 387--419 (2015; Zbl 1318.53092) Full Text: DOI arXiv OpenURL
Lee, Hyun Ho On the moduli space of a quantum Heisenberg manifold. (English) Zbl 1262.58006 J. Funct. Anal. 263, No. 4, 941-959 (2012). Reviewer: Haruo S. Suzuki (Sapporo) MSC: 58B34 58E15 46L87 PDF BibTeX XML Cite \textit{H. H. Lee}, J. Funct. Anal. 263, No. 4, 941--959 (2012; Zbl 1262.58006) Full Text: DOI OpenURL
Tart, Lauri Morita invariants for partially ordered semigroups with local units. (English) Zbl 1263.06006 Proc. Est. Acad. Sci. 61, No. 1, 38-47 (2012). Reviewer: Niovi Kehayopulu (Athenai) MSC: 06F05 20M10 PDF BibTeX XML Cite \textit{L. Tart}, Proc. Est. Acad. Sci. 61, No. 1, 38--47 (2012; Zbl 1263.06006) Full Text: DOI OpenURL
Tart, Lauri Conditions for strong Morita equivalence of partially ordered semigroups. (English) Zbl 1261.06019 Cent. Eur. J. Math. 9, No. 5, 1100-1113 (2011). Reviewer: Niovi Kehayopulu (Athenai) MSC: 06F05 20M10 PDF BibTeX XML Cite \textit{L. Tart}, Cent. Eur. J. Math. 9, No. 5, 1100--1113 (2011; Zbl 1261.06019) Full Text: DOI OpenURL
Gutt, Simone; Waldmann, Stefan Involutions and representations for reduced quantum algebras. (English) Zbl 1236.53070 Adv. Math. 224, No. 6, 2583-2644 (2010). MSC: 53D55 53D20 16D90 81S10 53D17 PDF BibTeX XML Cite \textit{S. Gutt} and \textit{S. Waldmann}, Adv. Math. 224, No. 6, 2583--2644 (2010; Zbl 1236.53070) Full Text: DOI arXiv Link OpenURL
Joiţa, Maria Stable outer conjugacy and strong Morita equivalence of group actions on pro-\(C^{*}\)-algebras. (English) Zbl 1182.46054 Cent. Eur. J. Math. 7, No. 1, 73-83 (2009). MSC: 46L55 46L05 46L08 PDF BibTeX XML Cite \textit{M. Joiţa}, Cent. Eur. J. Math. 7, No. 1, 73--83 (2009; Zbl 1182.46054) Full Text: DOI OpenURL
Ara, Pere; Mathieu, Martin; Ortega, Eduard The maximal \(C^*\)-algebra of quotients as an operator bimodule. (English) Zbl 1177.46040 Arch. Math. 92, No. 5, 405-413 (2009). MSC: 46L05 16D90 46A13 46H25 46L07 47L25 PDF BibTeX XML Cite \textit{P. Ara} et al., Arch. Math. 92, No. 5, 405--413 (2009; Zbl 1177.46040) Full Text: DOI arXiv OpenURL
Vlasenko, Mariya The graded ring of quantum theta functions for noncommutative torus with real multiplication. (English) Zbl 1123.14028 Int. Math. Res. Not. 2006, No. 5, Article ID 15825, 19 p. (2006). Reviewer: Arvid Siqveland (Kongsberg) MSC: 14L99 14A22 PDF BibTeX XML Cite \textit{M. Vlasenko}, Int. Math. Res. Not. 2006, No. 5, Article ID 15825, 19 p. (2006; Zbl 1123.14028) Full Text: DOI arXiv OpenURL
Kodaka, Kazunori \(C*\)-algebras that are isomorphic after tensoring and full projection. (English) Zbl 1075.46047 Proc. Edinb. Math. Soc., II. Ser. 47, No. 3, 659-668 (2004). MSC: 46L05 PDF BibTeX XML Cite \textit{K. Kodaka}, Proc. Edinb. Math. Soc., II. Ser. 47, No. 3, 659--668 (2004; Zbl 1075.46047) Full Text: DOI OpenURL
Blecher, David P. A Morita theorem for algebras of operators on Hilbert space. (English) Zbl 0984.47049 J. Pure Appl. Algebra 156, No. 2-3, 153-169 (2001). Reviewer: S.V.Kislyakov (St.Peterburg) MSC: 47L30 46M15 16D90 46L06 46L08 46L07 47L25 PDF BibTeX XML Cite \textit{D. P. Blecher}, J. Pure Appl. Algebra 156, No. 2--3, 153--169 (2001; Zbl 0984.47049) Full Text: DOI arXiv OpenURL
Bursztyn, Henrique; Waldmann, Stefan Deformation quantization of Hermitian vector bundles. (English) Zbl 0982.53073 Lett. Math. Phys. 53, No. 4, 349-365 (2000). MSC: 53D55 81R60 53D17 81S10 32L05 PDF BibTeX XML Cite \textit{H. Bursztyn} and \textit{S. Waldmann}, Lett. Math. Phys. 53, No. 4, 349--365 (2000; Zbl 0982.53073) Full Text: DOI arXiv OpenURL
Exel, Ruy Morita-Rieffel equivalence and spectral theory for integrable automorphism groups of \(C^*\)-algebras. (English) Zbl 0957.46040 J. Funct. Anal. 172, No. 2, 404-465 (2000). Reviewer: Khristo N.Boyadzhiev (Ada) MSC: 46L55 PDF BibTeX XML Cite \textit{R. Exel}, J. Funct. Anal. 172, No. 2, 404--465 (2000; Zbl 0957.46040) Full Text: DOI arXiv OpenURL
Kumjian, A. Notes on \(C^*\)-algebras of graphs. (English) Zbl 0945.46037 Ge, Liming (ed.) et al., Operator algebras and operator theory. Proceedings of the international conference, Shanghai, China, July 4-9, 1997. Providence, RI: American Mathematical Society. Contemp. Math. 228, 189-200 (1998). Reviewer: J.Hamhalter (Praha) MSC: 46L05 47L80 46L55 PDF BibTeX XML Cite \textit{A. Kumjian}, Contemp. Math. 228, 189--200 (1998; Zbl 0945.46037) OpenURL
Blecher, David P. A new approach to Hilbert \(C^*\)-modules. (English) Zbl 0874.46037 Math. Ann. 307, No. 2, 253-290 (1997). Reviewer: D.P.Blecher (Houston) MSC: 46L05 46H25 46L89 46M05 46M15 46C50 47L05 47L30 PDF BibTeX XML Cite \textit{D. P. Blecher}, Math. Ann. 307, No. 2, 253--290 (1997; Zbl 0874.46037) Full Text: DOI OpenURL
Talwar, S. Strong Morita equivalence and a generalisation of the Rees theorem. (English) Zbl 0855.20054 J. Algebra 181, No. 2, 371-394 (1996). Reviewer: U.Knauer (Oldenburg) MSC: 20M50 20M10 PDF BibTeX XML Cite \textit{S. Talwar}, J. Algebra 181, No. 2, 371--394 (1996; Zbl 0855.20054) Full Text: DOI OpenURL
Abadie, Beatriz Generalized fixed-point algebras of certain actions on crossed products. (English) Zbl 0856.46038 Pac. J. Math. 171, No. 1, 1-21 (1995). Reviewer: B.Abadie (Sao Paulo) MSC: 46L55 46L80 PDF BibTeX XML Cite \textit{B. Abadie}, Pac. J. Math. 171, No. 1, 1--21 (1995; Zbl 0856.46038) Full Text: DOI arXiv OpenURL
Bui, Huu Hung Full coactions on Hilbert \(C^*\)-modules. (English) Zbl 0852.46055 J. Aust. Math. Soc., Ser. A 59, No. 3, 409-420 (1995). MSC: 46L55 46H25 46L05 46L60 PDF BibTeX XML Cite \textit{H. H. Bui}, J. Aust. Math. Soc., Ser. A 59, No. 3, 409--420 (1995; Zbl 0852.46055) OpenURL
Bui, Huu Hung Morita equivalence of twisted crossed products. (English) Zbl 0844.46038 Proc. Am. Math. Soc. 123, No. 9, 2771-2776 (1995). MSC: 46L55 22D25 46L40 PDF BibTeX XML Cite \textit{H. H. Bui}, Proc. Am. Math. Soc. 123, No. 9, 2771--2776 (1995; Zbl 0844.46038) Full Text: DOI OpenURL
Beidar, K. I.; Mikhalev, A. V. Anti-isomorphism of endomorphism rings of modules and Morita anti-equivalence. (English. Russian original) Zbl 0845.16010 Russ. Math. Surv. 50, No. 1, 191-192 (1995); translation from Usp. Mat. Nauk 50, No. 1, 187-188 (1995). Reviewer: A.I.Kashu (Kishinev) MSC: 16D90 16S50 PDF BibTeX XML Cite \textit{K. I. Beidar} and \textit{A. V. Mikhalev}, Russ. Math. Surv. 50, No. 1, 191--192 (1995; Zbl 0845.16010); translation from Usp. Mat. Nauk 50, No. 1, 187--188 (1995) Full Text: DOI OpenURL
Brown, Lawrence G.; Pedersen, Gert K. On the geometry of the unit ball of a \(C^*\)-algebra. (English) Zbl 0834.46041 J. Reine Angew. Math. 469, 113-147 (1995). Reviewer: L.G.Brown (West Lafayette) MSC: 46L05 46L80 PDF BibTeX XML Cite \textit{L. G. Brown} and \textit{G. K. Pedersen}, J. Reine Angew. Math. 469, 113--147 (1995; Zbl 0834.46041) Full Text: DOI Crelle EuDML OpenURL
Walters, Samuel G. Strong Morita equivalence for the quasi-rotation \(C^*\)-algebras. (English) Zbl 0831.46076 J. Oper. Theory 31, No. 2, 327-349 (1994). Reviewer: H.Halpern (Cincinnati) MSC: 46L55 46L05 46L40 PDF BibTeX XML Cite \textit{S. G. Walters}, J. Oper. Theory 31, No. 2, 327--349 (1994; Zbl 0831.46076) OpenURL
Bui, Huu Hung Morita equivalence of twisted crossed products by coactions. (English) Zbl 0815.46059 J. Funct. Anal. 123, No. 1, 59-98 (1994). MSC: 46L55 PDF BibTeX XML Cite \textit{H. H. Bui}, J. Funct. Anal. 123, No. 1, 59--98 (1994; Zbl 0815.46059) Full Text: DOI OpenURL
Jeong, Ja A Full hereditary \(C^*\)-subalgebras of crossed products. (English) Zbl 0804.46079 Bull. Korean Math. Soc. 30, No. 2, 193-199 (1993). Reviewer: P.Milnes (London / Ontario) MSC: 46L55 PDF BibTeX XML Cite \textit{J. A Jeong}, Bull. Korean Math. Soc. 30, No. 2, 193--199 (1993; Zbl 0804.46079) OpenURL
Brown, Lawrence G.; Pedersen, Gert K. \(C^*\)-algebras of real rank zero. (English) Zbl 0776.46026 J. Funct. Anal. 99, No. 1, 131-149 (1991). MSC: 46L05 PDF BibTeX XML Cite \textit{L. G. Brown} and \textit{G. K. Pedersen}, J. Funct. Anal. 99, No. 1, 131--149 (1991; Zbl 0776.46026) Full Text: DOI OpenURL
Mikhalev, A. V. Isomorphisms of ring endomorphisms of modules that are close to free. (English. Russian original) Zbl 0711.16022 Mosc. Univ. Math. Bull. 44, No. 2, 28-38 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 2, 20-27 (1989). Reviewer: I.P.Shestakov MSC: 16S50 16D90 16W20 PDF BibTeX XML Cite \textit{A. V. Mikhalev}, Mosc. Univ. Math. Bull. 44, No. 2, 28--38 (1989; Zbl 0711.16022); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 2, 20--27 (1989) OpenURL
Rosenberg, Jonathan Continuous-trace algebras from the bundle theoretic point of view. (English) Zbl 0695.46031 J. Aust. Math. Soc., Ser. A 47, No. 3, 368-381 (1989). Reviewer: Do Ngoc Diep MSC: 46L80 46M20 18F25 46L35 55R10 46L05 PDF BibTeX XML Cite \textit{J. Rosenberg}, J. Aust. Math. Soc., Ser. A 47, No. 3, 368--381 (1989; Zbl 0695.46031) OpenURL
Johnson, S. R. Monoidal Morita equivalence. (English) Zbl 0693.18005 J. Pure Appl. Algebra 59, No. 2, 169-177 (1989). Reviewer: G.Călugăreanu MSC: 18D20 PDF BibTeX XML Cite \textit{S. R. Johnson}, J. Pure Appl. Algebra 59, No. 2, 169--177 (1989; Zbl 0693.18005) Full Text: DOI OpenURL
Packer, Judith A. Strong Morita equivalence for Heisenberg \(C^*\)-algebras and the positive cones of their \(K_ 0\)-groups. (English) Zbl 0647.46052 Can. J. Math. 40, No. 4, 833-864 (1988). Reviewer: J.A.Packer MSC: 46L55 46L80 47C15 PDF BibTeX XML Cite \textit{J. A. Packer}, Can. J. Math. 40, No. 4, 833--864 (1988; Zbl 0647.46052) Full Text: DOI OpenURL
Putnam, Ian F. Strong Morita equivalence for the Denjoy \(C^*\)-algebras. (English) Zbl 0627.46074 Can. Math. Bull. 31, No. 4, 439-447 (1988). MSC: 46L55 PDF BibTeX XML Cite \textit{I. F. Putnam}, Can. Math. Bull. 31, No. 4, 439--447 (1988; Zbl 0627.46074) Full Text: DOI OpenURL
Muhly, Paul S.; Renault, Jean N.; Williams, Dana P. Equivalence and isomorphism for groupoid \(C^*\)-algebras. (English) Zbl 0645.46040 J. Oper. Theory 17, 3-22 (1987). Reviewer: A.G.Baskakov MSC: 46L05 PDF BibTeX XML Cite \textit{P. S. Muhly} et al., J. Oper. Theory 17, 3--22 (1987; Zbl 0645.46040) OpenURL
Kumjian, Alexander On localizations and simple \(C^*\)-algebras. (English) Zbl 0574.46046 Pac. J. Math. 112, 141-192 (1984). MSC: 46L05 PDF BibTeX XML Cite \textit{A. Kumjian}, Pac. J. Math. 112, 141--192 (1984; Zbl 0574.46046) Full Text: DOI OpenURL
De Brabanter, Marc The classification of rotational rotation \(C^*\)-algebras. (English) Zbl 0539.46044 Arch. Math. 43, 79-83 (1984). MSC: 46L35 46L05 46L55 PDF BibTeX XML Cite \textit{M. De Brabanter}, Arch. Math. 43, 79--83 (1984; Zbl 0539.46044) Full Text: DOI OpenURL
Rieffel, Marc A. Applications of strong Morita equivalence to transformation group C*- algebras. (English) Zbl 0526.46055 Operator algebras and applications, Proc. Symp. Pure Math. 38, Part 1, 299-310 (1982). MSC: 46L05 54H20 46L55 22D15 PDF BibTeX XML OpenURL
Renault, Jean N. C*-algebras of groupoids and foliations. (English) Zbl 0501.46054 Operator algebras and applications, Proc. Symp. Pure Math. 38, Part 1, Kingston/Ont. 1980, 339-350 (1982). MSC: 46L05 18B40 57R30 PDF BibTeX XML OpenURL
Zettl, Heinrich H. Ideals in Hilbert modules and invariants under strong Morita equivalence of C*-algebras. (English) Zbl 0498.46034 Arch. Math. 39, 69-77 (1982). MSC: 46H10 46H25 46L05 46L35 PDF BibTeX XML Cite \textit{H. H. Zettl}, Arch. Math. 39, 69--77 (1982; Zbl 0498.46034) Full Text: DOI Backlinks: MO OpenURL