quantum-group: Exact symbolic verification of R-matrix and Yang--Baxter identities for $U_q(\mathfrak{sl}_2)$ and $GL_q(2|1)$
Year: 2026
Type: preprint
Abstract: Explicit R-matrices of quantum groups are routinely transcribed from the literature, yet whether they satisfy an identity depends on basis order, tensor placement, the coproduct and, for superalgebras, the Koszul sign rule. quantum-group is a Python package that builds such matrices exactly with SymPy and returns every identity as an exact residual matrix, whose nonzero entries locate the convention that disagrees. It covers U_q(sl_2) modules, tensor products and the fundamental R-matrix, and the graded Yang–Baxter equation for GL_q(2|1). Applied to the thesis it was written for, it exposed an R-matrix that satisfies the Yang–Baxter equation but intertwines the opposite coproduct. Userguide of quantum-group 1.1.1 (software: https://doi.org/10.5281/zenodo.23039671; source: https://github.com/TerekliTahaBerk/quantum-groups). Prepared for submission to SciPost Physics Codebases.
Source: arXiv (Cornell University)
Author: Terekli, Taha Berk
Institution: Yıldız Technical University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214731388