Finite Gröbner bases for quantum symmetric groups
Abstract
Non-commutative Gröbner bases of two-sided ideals are not necessarily finite. Motivated by this, we provide a closed-form description of a finite and reduced Gröbner bases for the two-sided ideal used in the construction of Wang's quantum symmetric group. In particular, this constructively proves that the word problem for quantum symmetric groups is decidable.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Polynomial and algebraic computation
Publication details
- Journal / source
- Journal of Symbolic Computation
- Volume
- 136
- Pages
- 102565–102565
- Publication date
- 10 February 2026
- Language
- EN