论文标题
有限组的组代数中存在非零痕量零群
Existence of Nonzero Trace-Zero Idempotents in the Group Algebras of Finite Groups
论文作者
论文摘要
让$ g $为有限的群体，$ k $一个特征性$ p> 0 $的$ g $的分裂字段。用$ kg $表示$ g $ $ k $和$ z（kg）$的集体代数为$ kg $的中心。令$ v_g $为$ k $ -subspace的$ kg $ trace-Zero元素。对于$ v_g $和$ v_g \ cap z（kg）$，我们给出了一些数值和必要的条件，以$ g $以上$ k $的$ g $的程度，为$ kg $的Mathieu子空间。相同的数值条件也表征了有限组$ g $，$ kg $没有非零跟踪零型群，而有限的组$ g $ $ kg $分别没有非零的中央trace-Zero diadempotents。
Let $G$ be a finite group and $K$ a splitting field of $G$ of characteristic $p>0$. Denote by $KG$ the group algebra of $G$ over $K$ and $Z(KG)$ the center of $KG$. Let $V_G$ be the $K$-subspace of trace-zero elements of $KG$. We give some numerical sufficient and necessary conditions for $V_G$ and $V_G\cap Z(KG)$, respectively, to be Mathieu subspaces of $KG$ in terms of the degrees of irreducible representations of $G$ over $K$. The same numerical conditions also characterize the finite groups $G$ that $KG$ has no nonzero trace-zero idempotents and the finite groups $G$ that $KG$ has no nonzero central trace-zero idempotents, respectively.
