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Zapiski Nauchnykh Seminarov LOMI, 1987, Volume 160, Pages 229–238
(Mi znsl5439)
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This article is cited in 1 scientific paper (total in 1 paper)
Some examples of semigroup algebras of finite representation type
I. S. Ponizovskii
Abstract:
The semigroup algebras over a field $K$ of the semigroups $T_n$ of all permutations of a set of $n$ elements are considered. It is proved: if $n\leq3$ and $(n!)^{-1}\in K$ then the algebra $KT_n$ has a finite representation type. Also the finiteness of the representation type of the semigroup algebra $KS$ is established, where $S$ is the sub-semigroup of $T_n$ ($n$ is arbitrary) such that $S=J_n\cup G$ where $J_n=\{x\in T_n|\operatorname{rank}x=1\}$, while $G$ is a doubly transitive subgroup of the symmetric group $S_n$, the order of $G$ being invertible in $K$.
Citation:
I. S. Ponizovskii, “Some examples of semigroup algebras of finite representation type”, Analytical theory of numbers and theory of functions. Part 8, Zap. Nauchn. Sem. LOMI, 160, "Nauka", Leningrad. Otdel., Leningrad, 1987, 229–238
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https://www.mathnet.ru/eng/znsl5439 https://www.mathnet.ru/eng/znsl/v160/p229
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Abstract page: | 164 | Full-text PDF : | 66 |
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