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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

Lapin, Sergey V.
Georgian Mathematical Journal , Volume 28 (6): 22 – Dec 1, 2021
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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2021-2098
Publisher site
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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 Journal – de Gruyter

Published: Dec 1, 2021

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

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