有单位交换环上对合$A_\infty$ -代数的具有$\infty$ -单形面的二面和自反模及二面和自反同调
Dihedral and reflexive modules with $\infty$-simplicial faces and dihedral and reflexive homology of involutive $A_\infty$-algebras over unital commutative rings
摘要：
引入了具有$\infty$ -单纯面的二面体和自反模的概念。对每一个对合$A_\infty$ -代数，构造了具有$\infty$ -单纯面的二面体和自反张量模.在对合$A_\infty$ -代数所定义的具有$\infty$ -单纯面的二面体模和自反模的基础上，给出了任何有单位的交换环上对合$A_\infty$ -代数的二面体模和自反同调模的构造.引入了对合同伦单位$A_\infty$ -代数的概念。构造了一个连接任何有单位的交换环上的对合同伦有单位的$A_\infty$ -代数的二面体与自反同调的长正合序列。
英文摘要：
The concepts of a dihedral and a reflexive module with $\infty$-simplicial faces are introduced. For each involutive $A_\infty$-algebra, the dihedral and the reflexive tensor modules with $\infty$-simplicial faces are constructed. On the basis of dihedral and reflexive modules with $\infty$-simplicial faces that defined by an involutive $A_\infty$-algebra the constructions of the dihedral and the reflexive homology of involutive $A_\infty$-algebras over any unital commutative rings are given. The conception of an involutive homotopy unital $A_\infty$-algebra is introduced. A long exact sequence that connecting the dihedral and the reflexive homology of involutive homotopically unital $A_\infty$-algebras over any unital commutative rings is constructed.
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