Cyclic Cohomology and Hopf Algebra Symmetry |
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Authors: | Connes Alain Moscovici Henri |
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Institution: | (1) Collège de France, 3 rue Ulm, 75005 Paris, France;(2) I.H.E.S., 35 route de Chartres, 91440 Bures-sur-Yvette, France;(3) Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, OH, 43210, U.S.A. |
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Abstract: | Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows the expansion of the range of applications of cyclic cohomology. It is the goal of this Letter to illustrate these recent developments, with special emphasis on the application to transverse index theory, and point towards future directions. In particular, we highlight the remarkable accord between our framework for cyclic cohomology of Hopf algebras on the one hand and both the algebraic as well as the analytic theory of quantum groups on the other, manifest in the construction of the modular square. |
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Keywords: | noncommutative geometry cyclic cohomology Hopf algebras quantum groups |
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