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arXiv · 1403.8076

Gr\"obner-Shirshov basis for the finitely presented algebras defined by permutation relations of symmetric type

Jianjun Qiu·Yuqun Chen
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Abstract

In this paper, we give a Gr\"obner-Shirshov basis for the finitely presented semigroup algebra $\mathbf{k}[S_n(Sym_n)]$ defined by permutation relations of symmetric type. As an application, by the Composition-Diamond Lemma, we obtain normal forms of elements of momoid $S_n(Sym_n)$, which gives an answer to an open problem posted by F. Ced\'o, E. Jespers and J. Okni\'nski [7] for the symmetric group case.

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Jianjun Qiu, Yuqun Chen. 2014-03-25. Gr\"obner-Shirshov basis for the finitely presented algebras defined by permutation relations of symmetric type. https://arxiv.org/abs/1403.8076

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