quantum-group: Exact SymPy verification of explicit U_q(sl_2) and GL_q(2|1) matrix identities

Abstract

quantum-group is a small Python package that builds the explicit matrices behind concrete quantum-group calculations with exact SymPy arithmetic and checks each identity as an exact residual matrix. A nonzero residual entry locates the convention that disagrees: basis order, tensor placement, coproduct or, for superalgebras, the Koszul sign rule. Covered: finite-dimensional Uq(sl2) modules and their defining relations; coproduct, counit and antipode with generator-level Hopf identities; tensor products and Clebsch–Gordan highest-weight vectors; the fundamental R-matrix with quantum Yang–Baxter, braid, Hecke and coproduct-intertwining checks, in the historical and the coproduct-compatible convention; and the graded Yang–Baxter equation for the 9×9 GLq(2|1) R-matrix of Çelik and Çelik (2021), including Rij placements on tensor powers via graded swaps. Scope: the checks are exact verifications on explicit finite-dimensional representations, not proofs in the abstract algebra, and the package is not a general quantum-group computer algebra system. This release (1.1.1) has the same package code and test suite as 1.1.0 (10.5281/zenodo.23015576). It adds the userguide prepared for SciPost Physics Codebases (scipost/; the same text as an amsart preprint in arxiv/), its worked examples with stored expected outputs, and a cross-check against data exported from GAP's QuaGroup package; continuous integration runs every example and compares its output. Records of earlier journal submissions, the thesis poster build and other material not needed for the software were removed from the repository; they remain in its Git history. Install: pip install quantum-group==1.1.1. Validate: python -m pytest (202 tests and doctests). Requires Python ≥ 3.10, SymPy ≥ 1.10, NetworkX ≥ 2.6, Matplotlib ≥ 3.5. Source, documentation and issues: github.com/TerekliTahaBerk/quantum-groups.