Bivariant K-theory of locally convex Z-graded algebras
Keywords:K-theory, Z-graded algebras, locally convex algebras, generalized Weyl algebras
In the present work, we describe some results about the K-theory of Z-graded algebras. First, in the context of C* algebras, we begin with the Pimsner-Voiculescu sequence for crossed products and its generalizations. We will see that there are results analog to these in the context of locally convex algebras and we conclude with results for generalized Weyl algebras.
Abadie B, Eilers S, Exel R. Morita equivalence for crossed products by Hilbert C*-bimodules. Trans. Amer. Math. Soc. 1998; 350(8):3043-3054.
Bavula V, Jordan D. Isomorphism problems and groups of automorphisms for generalized Weyl algebras, Trans. Amer. Math. Soc. 2001; 353(2):769-794.
Brzezínski T. Circle and line bundles over generalized Weyl algebras, Algebr. Represent. Theory. 2016; 19(1):57-69.
Cuntz J. K-theory and C*-algebras, Algebraic K-theory, number theory, geometry and analysis. in: Lecture Notes in Math., vol. 1046. Berlin: Springer; 1984; pp. 55-79.
Cuntz J. Bivariant K-theory and the Weyl algebra, K-Theory. 2005; 35(1-2):93-137.
Gabriel O, Grensing M. Six-term exact sequences for smooth generalized crossed products. J. Noncommut. Geom. 2013; 7(2):499-524.
Pimsner M, Voiculescu D. Exact Sequences forK-groups and Ext-groups for Certain Cross-product C?-algebras. J. of Operator Theory. 1980; 4(1):93-118.
Pimsner M. A class of C*-algebras generalizing both Cuntz-Krieger algebras and crossed products by Z. In: Free probability theory (Waterloo, ON, 1995), Fields Inst. Commun., vol. 12: Providence, RI Amer.Math. Soc. 1997; pp. 189-212.
Richard L, Solotar A. Isomorphisms between quantum generalized Weyl algebras, J. Algebra Appl. 2006; 5(3):271-285.
Ruy E. Circle actions on C*-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence, J. Funct. Anal. 1994; 122(2):361-401.
Valqui C, Gutierrez J. Bivariant K-theory of generalized Weyl algebras. J. of Noncommutative Geometry. 2020; 14(2):639-66.
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