PreprintCC BY 4.0arXiv
Graded Automorphism of Multiparameter Quantum Matrix Algebra
Abstract
We determine the graded automorphism group of the multiparameter quantum matrix algebra 𝒪λ,p(Mn(Bbbk)) over an arbitrary field Bbbk for all n≥2 and λ≠1. No other restrictions are assumed on p or λ. Every graded automorphism is a torus automorphism, possibly followed by transposition or by simultaneous reversal of the row and column indices. We give the precise parameter conditions for these two involutions. As an application, we also determine the full automorphism group when the multiplicative group generated by the parameters is torsion-free.
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BibTeX
@misc{jin2026graded,
title = {{Graded Automorphism of Multiparameter Quantum Matrix Algebra}},
author = {Hai Jin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39366},
eprint = {2610.39366},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39366},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Graded Automorphism of Multiparameter Quantum Matrix Algebra
AU - Hai Jin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39366
UR - https://arxiv.org/abs/2610.39366
AB - We determine the graded automorphism group of the multiparameter quantum matrix algebra 𝒪_λ,p(M_n(Bbbk)) over an arbitrary field Bbbk for all n≥2 and λ≠1. No other restrictions are assumed on p or λ. Every graded automorphism is a torus automorphism, possibly followed by transposition or by simultaneous reversal of the row and column indices. We give the precise parameter conditions for these two involutions. As an application, we also determine the full automorphism group when the multiplicative group generated by the parameters is torsion-free.
ER -