Finite Gr\"obner bases for quantum symmetric groups

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-19
Primary Topic
Algebraic structures and combinatorial models
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Finite Gr\"obner bases for quantum symmetric groups

ArXiv.org
Algebraic structures and combinatorial models
article

Finite Gr\"obner bases for quantum symmetric groups

article en

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.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Algebraic structures and combinatorial models
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Finite Gr\"obner bases for quantum symmetric groups · ArXiv.org (2025) | TGRS Research Map | TGRS