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arXiv · 2503.15104

Finite Gr\"obner bases for quantum symmetric groups

Leonard Schmitz·Marcel Wack
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Abstract

Non-commutative Gr\"obner bases of two-sided ideals are not necessarily finite. Motivated by this, we provide a closed-form description of a finite and reduced Gr\"obner bases for the two-sided ideal used in the construction of Wangs quantum symmetric group. In particular, this proves that the word problem for quantum symmetric groups is decidable.

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Leonard Schmitz, Marcel Wack. 2025-03-19. Finite Gr\"obner bases for quantum symmetric groups. https://arxiv.org/abs/2503.15104

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