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Operator algebras associated to modules over an integral domain. (English) Zbl 06848506

Summary: We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the \(C^*\)-envelope of the semicrossed product, and then consider properties of these algebras as models for studying general semicrossed products.

MSC:

47L40 Limit algebras, subalgebras of \(C^*\)-algebras
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References:

[1] W. Arveson, Operator algebras and measure preserving automorphisms, Acta Math. 118 (1967), 95-109. · Zbl 0182.18201
[2] W. Arveson and K. Josephson, Operator algebras and measure preserving automorphisms. II, J. Funct. Anal. 4 (1969), 100-134. · Zbl 0186.45903
[3] N. Brown and N. Ozawa, \(C^*\)-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88. American Mathematical Society, Providence, RI, 2008. · Zbl 1160.46001
[4] H. Choda, A correspondence between subgroups and subalgebras in a discrete \(C^*\)-crossed product, Math. Japonica 24 (1979), 225-229. · Zbl 0418.46049
[5] J. Cuntz and X. Li, The regular \(C^*\)-algebra of an integral domain, Quanta of maths, 149-170 Clay Math. Proc. 11 Amer. Math. Soc., Providence RI, 2010. · Zbl 1219.46059
[6] K. Davidson and E. Katsoulis, Isomorphisms between topological conjugacy algebras, J. Reine Angew. Math. 621 (2008), 29-51. · Zbl 1176.37007
[7] K. Davidson and E. Katsoulis, Semicrossed products of simple \(C^*\)-algebras, Math. Ann. 342 (2008), 515-525. · Zbl 1161.47057
[8] K. Davidson and E. Katsoulis, Operator algebras for multivariable dynamics, Mem. Amer. Math. Soc. 209 (2011), no. 982. · Zbl 1236.47001
[9] K. Davidson and E. Katsoulis, Dilation theory, commutant lifting, and semicrossed products, Doc. Math. 16 (2011), 781-868 · Zbl 1244.47063
[10] K. Davidson, A. Fuller, and E. Kakariadis, Semicrossed products of operator algebras by semigroups, Memoirs Amer. Math. Soc. 239 (201X). · Zbl 1385.47027
[11] B. Duncan, Operator algebras associated to integral domains, New York J. Math. 19 (2013), 39-50. · Zbl 1294.47097
[12] B. Duncan and J. Peters, Operator algebras and representations from commuting semigroup actions, J. Operator Theory 74 (2015), 23-43. · Zbl 1389.47111
[13] A. Fuller, Nonself-adjoint semicrossed products by abelian semigroups, Canad. J. Math. 65 (2013), 768-782. · Zbl 1352.47046
[14] E. Kakariadis and E. Katsoulis, Isomorphism invariants for multivariable \(C^*\)-dynamics, J. Noncommut. Geom. 8 (2014), 771-787.
[15] M. Landstad, D. Olesen, and G. Pedersen, Towards a Galois theory for crossed products of \(C^*\)-algebras, Math. Scand. 43 (1978), 311-321. · Zbl 0406.46056
[16] J. Peters, Semicrossed products of \(C^*\)-algebras, J. Funct. Anal. 59 (1984), 498-534. · Zbl 0636.46061
[17] J. Peters, The \(C^*\)-envelope of a semicrossed product and nest representations, Operator structures and dynamical systems, 197-215, Contemp. Math., 503, Amer. Math. Soc., Providence RI, 2009. · Zbl 1194.46096
[18] S. Roman, Advanced linear algebra, third edition, Graduate Texts in Mathematics, 135, Springer, New York, NY, 2008. · Zbl 1132.15002
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