Dihedral and reflexive modules with ∞-simplicial faces and dihedral and reflexive homology of involutive A_∞-algebras over unital commutative rings

2018/09/20 by Сергей Валерьевич 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.1809.07510

openalex publication_date 2018/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The concepts of a dihedral and a reflexive module with ∞-simplicial faces are introduced. For each involutive A_∞-algebra, the dihedral and the reflexive tensor modules with ∞-simplicial faces are constructed. On the basis of dihedral and reflexive modules with ∞-simplicial faces that defined by an involutive A_∞-algebra the constructions of the dihedral and the reflexive homology of involutive A_∞-algebras over any unital commutative rings are given. The conception of an involutive homotopy unital A_∞-algebra is introduced. A long exact sequence that connecting the dihedral and the reflexive homology of involutive homotopically unital A_∞-algebras over any unital commutative rings is constructed.

Citations

• A_∞ Algebras and the Cohomology of Moduli Spaces

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