# Homotopy invariance of the cyclic homology of A ∞-algebras under homotopy equivalences of A ∞-algebras

Homotopy invariance of the cyclic homology of A ∞-algebras under homotopy... AbstractIn the present paper, the cyclic homology functorfrom the category of A∞{A_{\infty}}-algebras over any commutativeunital ring K to the category of graded K-modules isconstructed. Further, it is shown that this functor sendshomotopy equivalences of A∞{A_{\infty}}-algebras into isomorphismsof graded modules. As a corollary, it is stated that the cyclichomology of an A∞{A_{\infty}}-algebra over any field is isomorphic tothe cyclic homology of the A∞{A_{\infty}}-algebra of homologies forthe source A∞{A_{\infty}}-algebra. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

# Homotopy invariance of the cyclic homology of A ∞-algebras under homotopy equivalences of A ∞-algebras

, Volume 28 (6): 22 – Dec 1, 2021
22 pages

/lp/de-gruyter/homotopy-invariance-of-the-cyclic-homology-of-a-algebras-under-qwGZEfxPHV
Publisher
de Gruyter
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2021-2098
Publisher site
See Article on Publisher Site

### Abstract

AbstractIn the present paper, the cyclic homology functorfrom the category of A∞{A_{\infty}}-algebras over any commutativeunital ring K to the category of graded K-modules isconstructed. Further, it is shown that this functor sendshomotopy equivalences of A∞{A_{\infty}}-algebras into isomorphismsof graded modules. As a corollary, it is stated that the cyclichomology of an A∞{A_{\infty}}-algebra over any field is isomorphic tothe cyclic homology of the A∞{A_{\infty}}-algebra of homologies forthe source A∞{A_{\infty}}-algebra.

### Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2021

Keywords: Cyclic homology; 55U10; 18G30; 55U43