Characteristic identities for orthogonal quantum matrices: examples
Abstract
In this note, we illustrate our recent results regarding structure theory of orthogonal Quantum Matrix algebras \cite{OP-BMW,OP-reciprocal,OP-ortho} using the simplest nontrivial example: the RTT-algebra associated with the canonical orthogonal R-matrix of type O(3) (see, e.g., \cite{FRT}). By introducing a suitable linear order on the set of generators, we obtain a set of quadratic relations defining the algebra. Next, we investigate relations among its higher-degree polynomials. As a result, we verify `in components' the Cayley-Hamilton and the reciprocal relations, obtained earlier with the use of the R-matrix techniques. We explicitly calculate the coefficients of the characteristic polynomials of quantum matrices and propose a conjecture regarding the form of the Hilbert-Poincaré series for the RTT-algebra.
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BibTeX
@misc{ogievetsky2026characteristic,
title = {{Characteristic identities for orthogonal quantum matrices: examples}},
author = {Oleg Ogievetsky and Pavel Pyatov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37813},
eprint = {2610.37813},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37813},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Characteristic identities for orthogonal quantum matrices: examples
AU - Oleg Ogievetsky
AU - Pavel Pyatov
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37813
UR - https://arxiv.org/abs/2610.37813
AB - In this note, we illustrate our recent results regarding structure theory of orthogonal Quantum Matrix algebras \cite{OP-BMW,OP-reciprocal,OP-ortho} using the simplest nontrivial example: the RTT-algebra associated with the canonical orthogonal R-matrix of type O(3) (see, e.g., \cite{FRT}). By introducing a suitable linear order on the set of generators, we obtain a set of quadratic relations defining the algebra. Next, we investigate relations among its higher-degree polynomials. As a result, we verify `in components' the Cayley-Hamilton and the reciprocal relations, obtained earlier with the use of the R-matrix techniques. We explicitly calculate the coefficients of the characteristic polynomials of quantum matrices and propose a conjecture regarding the form of the Hilbert-Poincaré series for the RTT-algebra.
ER -