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- W1750979427 abstract "The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}cdots a_{n} =a_{sigma (1)} a_{sigma (2)} cdots a_{sigma (n)}$, where $sigma$ runs through a subset $H$ of the symmetric group $text{Sym}_{n}$ of degree $n$, is investigated. Groups $H$ in which the cyclic group $langle (1,2, ldots ,n) rangle$ is a normal subgroup of index $2$ are considered. Certain representations by permutations of the dihedral and semidihedral groups belong to this class of groups. A normal form for the elements of the underlying monoid $S_n(H)$ with the same presentation as the algebra is obtained. Properties of the algebra are derived, it follows that it is an automaton algebra in the sense of Ufnarovskiu{i}. The universal group $G_n$ of $S_n(H)$ is a unique product group, and it is the central localization of a cancellative subsemigroup of $S_n(H)$. This, together with previously obtained results on such semigroups and algebras, is used to show that the algebra $K[S_n(H)]$ is semiprimitive." @default.
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- W1750979427 date "2016-02-01" @default.
- W1750979427 modified "2023-09-25" @default.
- W1750979427 title "Finitely presented algebras defined by permutation relations of dihedral type" @default.
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- W1750979427 doi "https://doi.org/10.1142/s0218196716500089" @default.
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