Double derivations and Cyclic homology

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dc.creatorGinzburg, Victor
dc.date2005-05-12
dc.date2005-08-11
dc.date.accessioned2026-07-07T05:19:49Z
dc.date.available2026-07-07T05:19:49Z
dc.descriptionWe 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.
dc.descriptionEntirely rewritten, additional results added, exposition simplified; 31pp
dc.identifierhttps://arxiv.org/abs/math/0505236
dc.identifierhttp://arxiv.org/abs/math/0505236
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75159
dc.subjectK-Theory and Homology
dc.subjectAlgebraic Geometry
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.titleDouble derivations and Cyclic homology
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