Double derivations and Cyclic homology

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We give a new construction of cyclic homology of an associative algebra A that does not involve Connes' differential. Our approach is based on an extended version of the complex ΩA, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any representation scheme Rep A. We define cyclic homology as the cohomology of the total complex (ΩA)[t], d+t \cdot i, arising from two anti-commuting differentials, d and i, on ΩA. The differential d, that replaces the Connes differential B, is the Karoubi-de Rham differential. The differential i that replaces the Hochschild differential b, is a map analogous to contraction with a vector field. This new map has no commutative counterpart.
Entirely rewritten, additional results added, exposition simplified; 31pp

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K-Theory and Homology, Algebraic Geometry, Quantum Algebra, Rings and Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/75159

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505236
 http://arxiv.org/abs/math/0505236

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arXiv