A new construction of cyclic homology
File(s)
Accepted version
Author(s)
Ginzburg, V
Schedler, TJ
Type
Journal Article
Abstract
Based on the ideas of Cuntz and Quillen, we give a simple construction of cyclic homology of unital algebras in terms of the noncommutative de Rham complex and a certain differential similar to the equivariant de Rham differential. We describe the Connes exact sequence in this setting. We define equivariant Deligne cohomology and construct, for each 𝑛⩾1 , a natural map from cyclic homology of an algebra to the GL𝑛 ‐equivariant Deligne cohomology of the variety of 𝑛 ‐dimensional representations of that algebra. The bridge between cyclic homology and equivariant Deligne cohomology is provided by extended cyclic homology, which we define and compute here, based on the extended noncommutative de Rham complex introduced previously by the authors.
Date Issued
2016-03-08
Date Acceptance
2015-12-13
Citation
Proceedings of the London Mathematical Society, 2016, 112 (3), pp.549-587
ISSN
0024-6115
Publisher
London Mathematical Society
Start Page
549
End Page
587
Journal / Book Title
Proceedings of the London Mathematical Society
Volume
112
Issue
3
Copyright Statement
© 2015 London Mathematical Society.
Sponsor
National Science Foundation
Identifier
https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms/pdw001
Grant Number
DMS-1406553
Subjects
0101 Pure Mathematics
0104 Statistics
Publication Status
Published
Date Publish Online
2016-03-08