The homotopy invariance of dihedral homology of involutive $A_{\infty }$-algebras over rings

Abstract

The dihedral homology functor $HD:A_{\infty }^{\mathrm{inv}}(K)\to GrM(K)$ from the category $A_{\infty }^{\mathrm{inv}}(K)$ of involutive $A_{\infty }$-algebras over any commutative unital ring $K$ to the category $GrM(K)$ of graded $K$-modules is constructed. Further, it is showed that this functor sends homotopy equivalences of involutive $A_{\infty }$-algebras into isomorphisms of graded modules.

arXiv admin note: substantial text overlap with arXiv:1905.10991, arXiv:1809.07510

References in corpus (1)

• The homotopy invariance of cyclic homology of $A_{\infty }$-algebras over rings