部分表示与部分群代数
Partial Representations and Partial Group Algebras
摘要：
域K上群G的部分群代数记为K_{par}（G），是其表示对应于G在K-向量空间上的部分表示的代数。本文研究了部分群代数K_{par}（G）的结构，其中G是有限群.特别地，给定两个有限阿贝尔群G_1和G_2，我们证明了：如果K的特征为零，则K_{par}（G_1）同构于K_{par}（G_2）当且仅当G_1同构于G_2.
英文摘要：
The partial group algebra of a group G over a field K, denoted by K_{par}(G), is the algebra whose representations correspond to the partial representations of G over K-vector spaces. In this paper we study the structure of the partial group algebra K_{par}(G), where G is a finite group. In particular, given two finite abelian groups G_1 and G_2, we prove that if the characteristic of K is zero, then K_{par}(G_1) is isomorphic to K_{par}(G_2) if and only if G_1 is isomorphic to G_2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
