Brubaker, Ben; Buciumas, Valentin; Bump, Daniel; Gustafsson, Henrik P. A. Vertex operators, solvable lattice models and metaplectic Whittaker functions. (English) Zbl 07286851 Commun. Math. Phys. 380, No. 2, 535-579 (2020). Reviewer: Piotr Garbaczewski (Opole) MSC: 82B20 33C15 16T05 16T25 20G42 33D80 17B69 17B80 37K60 15A66 PDF BibTeX XML Cite \textit{B. Brubaker} et al., Commun. Math. Phys. 380, No. 2, 535--579 (2020; Zbl 07286851) Full Text: DOI
Liu, Guohua; Wang, Wei; Wang, Shuanhong; Zhang, Xiaohui A braided \(T\)-category over weak monoidal Hom-Hopf algebras. (English) Zbl 07272220 J. Algebra Appl. 19, No. 8, Article ID 2050159, 28 p. (2020). MSC: 16T05 18M15 PDF BibTeX XML Cite \textit{G. Liu} et al., J. Algebra Appl. 19, No. 8, Article ID 2050159, 28 p. (2020; Zbl 07272220) Full Text: DOI
Burciu, Sebastian Conjugacy classes and centralizers for pivotal fusion categories. (English) Zbl 1448.18025 Monatsh. Math. 193, No. 1, 13-46 (2020). Reviewer: Andrew Schopieray (Vancouver) MSC: 18M20 16T05 19D23 PDF BibTeX XML Cite \textit{S. Burciu}, Monatsh. Math. 193, No. 1, 13--46 (2020; Zbl 1448.18025) Full Text: DOI
Faitg, Matthieu Projective representations of mapping class groups in combinatorial quantization. (English) Zbl 1448.58008 Commun. Math. Phys. 377, No. 1, 161-198 (2020). Reviewer: Alexander Schmeding (Bergen) MSC: 58D05 81S99 53D50 PDF BibTeX XML Cite \textit{M. Faitg}, Commun. Math. Phys. 377, No. 1, 161--198 (2020; Zbl 1448.58008) Full Text: DOI
Weber, Thomas Braided Cartan calculi and submanifold algebras. (English) Zbl 1437.18010 J. Geom. Phys. 150, Article ID 103612, 24 p. (2020). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 18M15 16T05 17B37 58B34 58A15 PDF BibTeX XML Cite \textit{T. Weber}, J. Geom. Phys. 150, Article ID 103612, 24 p. (2020; Zbl 1437.18010) Full Text: DOI
Xiao, Zhankui; Yang, Yuping; Zhang, Yinhuo The diagram category of framed tangles and invariants of quantized symplectic group. (English) Zbl 1441.18022 Sci. China, Math. 63, No. 4, 689-700 (2020). Reviewer: Paolo Saracco (Bruxelles) MSC: 18M15 17B37 16T30 20G05 PDF BibTeX XML Cite \textit{Z. Xiao} et al., Sci. China, Math. 63, No. 4, 689--700 (2020; Zbl 1441.18022) Full Text: DOI
Halbig, Sebastian; Krähmer, Ulrich A Hopf algebra without a modular pair in involution. (English) Zbl 07215861 Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVII. Workshop and summer school, Białowieża, Poland, July 1–7, 2018. Dedicated to Daniel Sternheimer on the occasion of his 80th birthday. Cham: Birkhäuser (ISBN 978-3-030-34071-1/hbk; 978-3-030-34072-8/ebook). Trends in Mathematics, 140-142 (2019). Reviewer: Leandro Vendramin (Buenos Aires) MSC: 16T05 PDF BibTeX XML Cite \textit{S. Halbig} and \textit{U. Krähmer}, in: Geometric methods in physics XXXVII. Workshop and summer school, Białowieża, Poland, July 1--7, 2018. Dedicated to Daniel Sternheimer on the occasion of his 80th birthday. Cham: Birkhäuser. 140--142 (2019; Zbl 07215861) Full Text: DOI
Shimizu, Kenichi Non-degeneracy conditions for braided finite tensor categories. (English) Zbl 1433.18011 Adv. Math. 355, Article ID 106778, 36 p. (2019). Reviewer: Zhiqiang Yu (Shanghai) MSC: 18M15 18M20 16T05 PDF BibTeX XML Cite \textit{K. Shimizu}, Adv. Math. 355, Article ID 106778, 36 p. (2019; Zbl 1433.18011) Full Text: DOI
Cheng, Raymond; Jackson, David M.; Stanley, Geoff J. Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak {sl}_{n+1}\). (English) Zbl 1403.05163 Ann. Comb. 22, No. 4, 681-710 (2018). MSC: 05E15 17B37 16T05 PDF BibTeX XML Cite \textit{R. Cheng} et al., Ann. Comb. 22, No. 4, 681--710 (2018; Zbl 1403.05163) Full Text: DOI
van der Veen, Roland Introduction to quantum invariants of knots. (English) Zbl 1403.57011 Wood, David R. (ed.) et al., 2016 MATRIX annals. Cham: Springer (ISBN 978-3-319-72298-6/hbk; 978-3-319-72299-3/ebook). MATRIX Book Series 1, 637-656 (2018). MSC: 57M27 57-02 PDF BibTeX XML Cite \textit{R. van der Veen}, MATRIX Book Ser. 1, 637--656 (2018; Zbl 1403.57011) Full Text: DOI
Huang, Hua-Lin; Yang, Yuping; Zhang, Yinhuo On nondiagonal finite quasi-quantum groups over finite abelian groups. (English) Zbl 06976962 Sel. Math., New Ser. 24, No. 5, 4197-4221 (2018). MSC: 16T20 16T05 18M15 PDF BibTeX XML Cite \textit{H.-L. Huang} et al., Sel. Math., New Ser. 24, No. 5, 4197--4221 (2018; Zbl 06976962) Full Text: DOI
De Renzi, Marco; Geer, Nathan; Patureau-Mirand, Bertrand Renormalized Hennings invariants and \(2+1\)-TQFTs. (English) Zbl 1402.57024 Commun. Math. Phys. 362, No. 3, 855-907 (2018). Reviewer: Sergiy Koshkin (Houston) MSC: 57R56 81T45 PDF BibTeX XML Cite \textit{M. De Renzi} et al., Commun. Math. Phys. 362, No. 3, 855--907 (2018; Zbl 1402.57024) Full Text: DOI
Lentner, Simon; Mierach, Svea Nora; Schweigert, Christoph; Sommerhäuser, Yorck Hochschild cohomology and the modular group. (English) Zbl 1446.16013 J. Algebra 507, 400-420 (2018). Reviewer: Angela Gammella-Mathieu (Metz) MSC: 16E40 16T05 PDF BibTeX XML Cite \textit{S. Lentner} et al., J. Algebra 507, 400--420 (2018; Zbl 1446.16013) Full Text: DOI
Sartori, Antonio The Alexander polynomial as quantum invariant of links. (English) Zbl 1329.57021 Ark. Mat. 53, No. 1, 177-202 (2015). Reviewer: Kazuo Habiro (Kyoto) MSC: 57M27 57M25 17B37 PDF BibTeX XML Cite \textit{A. Sartori}, Ark. Mat. 53, No. 1, 177--202 (2015; Zbl 1329.57021) Full Text: DOI arXiv
Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C. Ribbon Hopf algebras from group character rings. (English) Zbl 1308.16027 Linear Multilinear Algebra 62, No. 6, 749-775 (2014). Reviewer: Loïc Foissy (Calais) MSC: 16T05 05E05 11E57 43A40 57M25 16T30 PDF BibTeX XML Cite \textit{B. Fauser} et al., Linear Multilinear Algebra 62, No. 6, 749--775 (2014; Zbl 1308.16027) Full Text: DOI arXiv
Neshveyev, Sergey; Tuset, Lars Compact quantum groups and their representation categories. (English) Zbl 1316.46003 Cours Spécialisés (Paris) 20. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-777-3/hbk). iv, 169 p. (2013). Reviewer: Jörg Feldvoss (Mobile) MSC: 46-02 46L65 46L89 22E46 16T20 17B37 20G42 18D99 PDF BibTeX XML Cite \textit{S. Neshveyev} and \textit{L. Tuset}, Compact quantum groups and their representation categories. Paris: Société Mathématique de France (SMF) (2013; Zbl 1316.46003)
Davydov, Alexei; Runkel, Ingo \(\mathbb Z/2\mathbb Z\)-extensions of Hopf algebra module categories by their base categories. (English) Zbl 1328.18009 Adv. Math. 247, 192-265 (2013). Reviewer: Daniel Bulacu (Bucharest) MSC: 18D10 16T05 PDF BibTeX XML Cite \textit{A. Davydov} and \textit{I. Runkel}, Adv. Math. 247, 192--265 (2013; Zbl 1328.18009) Full Text: DOI arXiv
Kauffman, Louis H. Knots and physics. 4th ed. (English) Zbl 1266.57001 Series on Knots and Everything 53. Singapore: World Scientific (ISBN 978-981-4383-00-4/hbk; 978-981-4383-01-1/pbk). xviii, 846 p. (2013). Reviewer: Claus Ernst (Bowling Green) MSC: 57-01 81-01 57M25 57M15 57Q35 81R10 81R25 92D20 17B37 16W99 94C99 PDF BibTeX XML Cite \textit{L. H. Kauffman}, Knots and physics. 4th ed. Singapore: World Scientific (2013; Zbl 1266.57001)
Fuchs, Jürgen; Schweigert, Christoph; Stigner, Carl Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms. (English) Zbl 1296.16029 J. Algebra 363, 29-72 (2012). Reviewer: Jörg Feldvoss (Mobile) MSC: 16T05 17B81 18D10 57M50 81T40 PDF BibTeX XML Cite \textit{J. Fuchs} et al., J. Algebra 363, 29--72 (2012; Zbl 1296.16029) Full Text: DOI arXiv
Bobtcheva, Ivelina; Piergallini, Riccardo On 4-dimensional 2-handlebodies and 3-manifolds. (English) Zbl 1276.57010 J. Knot Theory Ramifications 21, No. 12, 1250110, 230 p. (2012). Reviewer: Motoo Tange (Tsukuba) MSC: 57M27 16T05 57R56 16W99 17B37 18D35 PDF BibTeX XML Cite \textit{I. Bobtcheva} and \textit{R. Piergallini}, J. Knot Theory Ramifications 21, No. 12, 1250110, 230 p. (2012; Zbl 1276.57010) Full Text: DOI arXiv
Hu, Naihong; Wang, Xiuling Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type \(B\). (English) Zbl 1263.17014 J. Geom. Phys. 60, No. 3, 430-453 (2010). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B37 16T20 PDF BibTeX XML Cite \textit{N. Hu} and \textit{X. Wang}, J. Geom. Phys. 60, No. 3, 430--453 (2010; Zbl 1263.17014) Full Text: DOI arXiv
Snyder, Noah; Tingley, Peter The half-twist for \(U_q(\mathfrak g)\) representations. (English) Zbl 1241.17019 Algebra Number Theory 3, No. 7, 809-834 (2009). Reviewer: Earl J. Taft (New Brunswick) MSC: 17B37 16T99 PDF BibTeX XML Cite \textit{N. Snyder} and \textit{P. Tingley}, Algebra Number Theory 3, No. 7, 809--834 (2009; Zbl 1241.17019) Full Text: DOI Link arXiv
Hadfield, Tom; Krähmer, Ulrich Braided homology of quantum groups. (English) Zbl 1188.58005 J. \(K\)-Theory 4, No. 2, 299-332 (2009). Reviewer: Akira Asada (Takarazuka) MSC: 58B32 19D55 16T05 16T10 16T15 PDF BibTeX XML Cite \textit{T. Hadfield} and \textit{U. Krähmer}, J. \(K\)-Theory 4, No. 2, 299--332 (2009; Zbl 1188.58005) Full Text: DOI arXiv
Hu, Naihong; Wang, Xiuling Convex PBW-type Lyndon basis and restricted two-parameter quantum groups of type \(G_2\). (English) Zbl 1216.17012 Pac. J. Math. 241, No. 2, 243-273 (2009). Reviewer: Olaf Ninnemann (Berlin) MSC: 17B37 16T20 PDF BibTeX XML Cite \textit{N. Hu} and \textit{X. Wang}, Pac. J. Math. 241, No. 2, 243--273 (2009; Zbl 1216.17012) Full Text: DOI Link arXiv
Frohman, Charles; Kania-Bartoszynska, Joanna A matrix model for quantum \(SL_2\). (English) Zbl 1028.81029 Radford, David E. (ed.) et al., Diagrammatic morphisms and applications. AMS special session on diagrammatic morphisms in algebra, category theory, and topology, San Francisco, CA, USA, October 21-22, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 318, 107-112 (2003). MSC: 81R50 17B37 57M27 PDF BibTeX XML Cite \textit{C. Frohman} and \textit{J. Kania-Bartoszynska}, Contemp. Math. 318, 107--112 (2003; Zbl 1028.81029) Full Text: arXiv
Takeuchi, Mitsuhiro Modular categories and Hopf algebras. (English) Zbl 0995.16032 J. Algebra 243, No. 2, 631-643 (2001). Reviewer: Goutam Mukherjee (Kolkata) MSC: 16W30 18D10 57T05 PDF BibTeX XML Cite \textit{M. Takeuchi}, J. Algebra 243, No. 2, 631--643 (2001; Zbl 0995.16032) Full Text: DOI
Nenciu, Adriana Quasitriangular structures for a class of pointed Hopf algebras constructed by Ore extensions. (English) Zbl 0991.16035 Commun. Algebra 29, No. 8, 3419-3432 (2001). Reviewer: Sonia Natale (Paris) MSC: 16W30 16S36 PDF BibTeX XML Cite \textit{A. Nenciu}, Commun. Algebra 29, No. 8, 3419--3432 (2001; Zbl 0991.16035) Full Text: DOI
Kauffman, Louis H. Right integrals and invariants of three-manifolds. (English) Zbl 0951.57005 Hass, Joel (ed.) et al., Proceedings of the Kirbyfest, Berkeley, CA, USA, June 22-26, 1998. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 2, 215-232 (1999). Reviewer: Vincent Blanloeil (Strasbourg) MSC: 57M27 57N10 57M50 57T05 PDF BibTeX XML Cite \textit{L. H. Kauffman}, Geom. Topol. Monogr. 2, 215--232 (1999; Zbl 0951.57005) Full Text: EMIS arXiv
Etingof, Pavel; Kazhdan, David Quantization of Lie bialgebras. II, III. (English) Zbl 0915.17009 Sel. Math., New Ser. 4, No. 2, 213-231 (1998); 4, No. 2, 233-269 (1998). Reviewer: Earl J.Taft (New Brunswick) MSC: 17B37 17B62 16T05 18M15 PDF BibTeX XML Cite \textit{P. Etingof} and \textit{D. Kazhdan}, Sel. Math., New Ser. 4, No. 2, 213--231 (1998); 4, No. 2, 233--269 (1998; Zbl 0915.17009) Full Text: DOI arXiv
Abdesselam, Boucif The twisted Heisenberg algebra \({\mathcal U}_{h,w}({\mathcal H}(4))\). (English) Zbl 0897.17015 J. Math. Phys. 38, No. 12, 6045-6060 (1997). MSC: 17B37 16W30 81R50 57M25 PDF BibTeX XML Cite \textit{B. Abdesselam}, J. Math. Phys. 38, No. 12, 6045--6060 (1997; Zbl 0897.17015) Full Text: DOI arXiv
Krob, Daniel; Thibon, Jean-Yves Noncommutative symmetric functions. IV: Quantum linear groups and Hecke algebras at \(q=0\). (English) Zbl 0881.05120 J. Algebr. Comb. 6, No. 4, 339-376 (1997). MSC: 05E05 20C30 PDF BibTeX XML Cite \textit{D. Krob} and \textit{J.-Y. Thibon}, J. Algebr. Comb. 6, No. 4, 339--376 (1997; Zbl 0881.05120) Full Text: DOI
Häring-Oldenburg, Reinhard Reconstruction of weak quasi Hopf algebras. (English) Zbl 0882.18009 J. Algebra 194, No. 1, 14-35 (1997). Reviewer: R.H.Street (North Ryde) MSC: 18D35 16W30 PDF BibTeX XML Cite \textit{R. Häring-Oldenburg}, J. Algebra 194, No. 1, 14--35 (1997; Zbl 0882.18009) Full Text: DOI
Leduc, Robert; Ram, Arun A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras: The Brauer, Birman-Wenzl, and type A Iwahori-Hecke algebras. (English) Zbl 0936.17016 Adv. Math. 125, No. 1, 1-94 (1997). MSC: 17B37 16W30 57M25 20C15 PDF BibTeX XML Cite \textit{R. Leduc} and \textit{A. Ram}, Adv. Math. 125, No. 1, 1--94 (1997; Zbl 0936.17016) Full Text: DOI
Hennings, Mark Invariants of links and 3-manifolds obtained from Hopf algebras. (English) Zbl 0882.57002 J. Lond. Math. Soc., II. Ser. 54, No. 3, 594-624 (1996). Reviewer: H.Murakami (Tokyo) MSC: 57M25 57N10 PDF BibTeX XML Cite \textit{M. Hennings}, J. Lond. Math. Soc., II. Ser. 54, No. 3, 594--624 (1996; Zbl 0882.57002) Full Text: DOI
Hayashi, Nobuharu Graph invariants of Vassiliev type and application to 4D quantum gravity. (English) Zbl 0858.57005 Commun. Math. Phys. 180, No. 3, 653-670 (1996). MSC: 57M15 83C47 PDF BibTeX XML Cite \textit{N. Hayashi}, Commun. Math. Phys. 180, No. 3, 653--670 (1996; Zbl 0858.57005) Full Text: DOI arXiv
Etingof, Pavel; Kazhdan, David Quantization of Lie bialgebras. I. (English) Zbl 0863.17008 Sel. Math., New Ser. 2, No. 1, 1-41 (1996). Reviewer: Earl J.Taft (New Brunswick) MSC: 17B37 17B62 16T05 18M15 PDF BibTeX XML Cite \textit{P. Etingof} and \textit{D. Kazhdan}, Sel. Math., New Ser. 2, No. 1, 1--41 (1996; Zbl 0863.17008) Full Text: DOI arXiv
Majid, Shahn; Rodríguez-Plaza, M. J. Nonstandard quantum groups and superization. (English) Zbl 0856.17015 J. Math. Phys. 36, No. 12, 7081-7097 (1995). Reviewer: Yu.N.Bespalov (Kiev) MSC: 17B37 16W30 81R50 18D20 16W55 PDF BibTeX XML Cite \textit{S. Majid} and \textit{M. J. Rodríguez-Plaza}, J. Math. Phys. 36, No. 12, 7081--7097 (1995; Zbl 0856.17015) Full Text: DOI
Lyubashenko, Volodymyr V. Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity. (English) Zbl 0844.57016 Commun. Math. Phys. 172, No. 3, 467-516 (1995). MSC: 57N10 17B37 PDF BibTeX XML Cite \textit{V. V. Lyubashenko}, Commun. Math. Phys. 172, No. 3, 467--516 (1995; Zbl 0844.57016) Full Text: DOI arXiv
Gelfand, Israel M.; Krob, Daniel; Lascoux, Alain; Leclerc, Bernard; Retakh, Vladimir S.; Thibon, Jean-Yves Noncommutative symmetric functions. (English) Zbl 0831.05063 Adv. Math. 112, No. 2, 218-348 (1995). Reviewer: V.A.Ufnarovski (Lund) MSC: 05E05 05E10 15A09 15A15 41A21 68Q70 16W30 PDF BibTeX XML Cite \textit{I. M. Gelfand} et al., Adv. Math. 112, No. 2, 218--348 (1995; Zbl 0831.05063) Full Text: DOI
Turaev, V. G. Quantum invariants of knots and 3-manifolds. (English) Zbl 0812.57003 de Gruyter Studies in Mathematics. 18. Berlin: Walter de Gruyter. x, 588 p. (1994). Reviewer: L.P.Neuwirth (Princeton) MSC: 57-02 57N10 57M25 81R50 18D10 18D20 18D35 57N13 17B37 PDF BibTeX XML Cite \textit{V. G. Turaev}, Quantum invariants of knots and 3-manifolds. Berlin: Walter de Gruyter (1994; Zbl 0812.57003)
Kauffman, Louis H. Gauss codes, quantum groups and ribbon Hopf algebras. (English) Zbl 0803.57001 Rev. Math. Phys. 5, No. 4, 735-773 (1993). Reviewer: H.R.Morton (Liverpool) MSC: 57M25 16W30 17B37 PDF BibTeX XML Cite \textit{L. H. Kauffman}, Rev. Math. Phys. 5, No. 4, 735--773 (1993; Zbl 0803.57001) Full Text: DOI
Ohtsuki, Tomotada Colored ribbon Hopf algebras and universal invariants of framed links. (English) Zbl 0798.57006 J. Knot Theory Ramifications 2, No. 2, 211-232 (1993). Reviewer: H.Murakami (Osaka) MSC: 57M25 82B23 17B37 81R50 PDF BibTeX XML Cite \textit{T. Ohtsuki}, J. Knot Theory Ramifications 2, No. 2, 211--232 (1993; Zbl 0798.57006) Full Text: DOI
Kauffman, Louis H.; Radford, David E. A necessary and sufficient condition for a finite-dimensional Drinfel’d double to be a ribbon Hopf algebra. (English) Zbl 0802.16035 J. Algebra 159, No. 1, 98-114 (1993). Reviewer: E.J.Taft (New Brunswick) MSC: 16W30 PDF BibTeX XML Cite \textit{L. H. Kauffman} and \textit{D. E. Radford}, J. Algebra 159, No. 1, 98--114 (1993; Zbl 0802.16035) Full Text: DOI
Cotta-Ramusino, Paolo; Rinaldi, Maurizio Multi-parameter quantum groups related to link-diagrams. (English) Zbl 0776.17002 Commun. Math. Phys. 142, No. 3, 589-604 (1991). Reviewer: H.H.Andersen (Aarhus) MSC: 17B37 16W30 57M25 PDF BibTeX XML Cite \textit{P. Cotta-Ramusino} and \textit{M. Rinaldi}, Commun. Math. Phys. 142, No. 3, 589--604 (1991; Zbl 0776.17002) Full Text: DOI
Reshetikhin, N. Yu.; Turaev, V. G. Ribbon graphs and their invariants derived from quantum groups. (English) Zbl 0768.57003 Commun. Math. Phys. 127, No. 1, 1-26 (1990). Reviewer: J.H.Przytycki (Riverside) MSC: 57M25 81R05 17B37 81T40 16W30 PDF BibTeX XML Cite \textit{N. Yu. Reshetikhin} and \textit{V. G. Turaev}, Commun. Math. Phys. 127, No. 1, 1--26 (1990; Zbl 0768.57003) Full Text: DOI