2019/05/27 by С. В. Лапин, Lapin, S. V.
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1905.10991
openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper the cyclic homology functor from the category of A_∞-algebras over any commutative unital ring K to the category of graded K-modules is constructed. Further, it is showed that this functor sends homotopy equivalences of A_∞-algebras into isomorphisms of graded modules. As a corollary, it is obtained that the cyclic homology of an A_∞-algebra over any field is isomorphic to the cyclic homology of the A_∞-algebra of homologies for the source A_∞-algebra.