A module structure on cyclic cohomology of group graded algebras |
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Authors: | Ronghui Ji |
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Institution: | (1) Department of Mathematical Sciences, Indiana University — Purdue University at Indianapolis, 402 N. Blackford Street, 46202-3216 Indianapolis, IN, USA |
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Abstract: | Letk be a field of characteristic 0, and letB be an algebra overk which is graded by a discrete groupG. Let HC*(A) denote the cyclic cohomology of an algebraA overk. We prove that there is an HC*(kG)-module structure on HC*(B) which generalizes Connes' periodicity operator on HC*(B). This module structure also decomposes with respect to conjugacy classes and results in a natural generalization of the results of Burghelea and Nistor in the cases of group algebras and algebraic crossed product algebras, respectively. Moreover, the proofs given in this paper are purely analytic with explicit constructions which can be used in the calculation of the cyclic cohomology of topological twisted crossed product algebras.Research sponsored in part by NSF Grant DMS-9204005. |
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Keywords: | K-Theory cyclic cohomology module structure group graded algebras twisted crossed products |
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