Hom-群、表示与同调代数
Hom-Groups, Representations and Homological Algebra
摘要：
Hom群G是群的非结合版本，其中结合性、可逆性和酉性被映射α扭曲：G \longrightarrow G。引入Hom-群代数KG，我们发现Hom-群是Homalgebra，Hom-李代数和Hom-霍普夫代数的例子.我们在Hom-群G上引入了两类模。为了进一步了解这些模，我们引入了系数为这些模的Hom-群（上）同调。我们的（余）同调论推广了群的群（余）同调。尽管结合的情况下，我们观察到的系数的Hom-group的同调是不同的，从Hom-group的上同调。我们证明了逆元提供了左、右G-模中的系数与Hom-群（上）同调之间的关系。证明了我们关于系数Hom-群的（余）同调论可化为Hom-群代数的Hochschild（余）同调.对于某些系数，Hom-群（上）同调的函性将被证明。
英文摘要：
A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map α: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples of Homalgebras, Hom-Lie algebras and Hom-Hopf algebras. We introduce two types of modules over a Hom-group G. To find out more about these modules, we introduce Hom-group (co)homology with coefficients in these modules. Our (co)homology theories generalizes group (co)homologies for groups. Despite the associative case we observe that the coefficients of Hom-group homology is different from the ones for Hom-group cohomology. We show that the inverse elements provide a relation between Hom-group (co)homology with coefficients in right and left G-modules. It will be shown that our (co)homology theories for Hom-groups with coefficients could be reduced to the Hochschild (co)homologies of Hom-group algebras. For certain coefficients the functoriality of Hom-group (co)homology will be shown.
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