Computation of Wedderburn decomposition of groups algebras from their subalgebra
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In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra $\mathbb{F}_qG$ can be deduced from a subalgebra $\mathbb{F}_q(G/H)$ of factor group $G/H$ of $G$, where $H$ is a normal subgroup of $G$ of prime order $P$. Here, we assume that $q=p^r$ for some prime $p$ and the center of each Wedderburn component of $\mathbb{F}_qG$ is the coefficient field $\mathbb{F}_q$.
Abstract
In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra $\mathbb{F}_qG$ can be deduced from a subalgebra $\mathbb{F}_q(G/H)$ of factor group $G/H$ of $G$, where $H$ is a normal subgroup of $G$ of prime order $P$. Here, we assume that $q=p^r$ for some prime $p$ and the center of each Wedderburn component of $\mathbb{F}_qG$ is the coefficient field $\mathbb{F}_q$.
참고문헌 (7)
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