Hopf Modules and Noncommutative Differential Geometry |
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Authors: | Atabey Kaygun Masoud Khalkhali |
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Affiliation: | (1) Department of Mathematics, The University of Western Ontario, London, Ontario, N6A 5B7, Canada |
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Abstract: | We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter–Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as “flat bundles” in the sense of Connes’ noncommutative differential geometry. |
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Keywords: | noncommutative differential geometry Hopf cyclic cohomology Hopf algebras flat bundles |
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