Determinants in Quantum Matrix Algebras and Integrable Systems
Abstract
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used in the theory of integrable systems. Also, we generalize the quantum integrable spin systems from [CFRS] by using generalized Yangians, related to couples of compatible braidings. We demonstrate that such quantum integrable spin systems are not uniquely determined by the "quantum coordinate ring" of the basic space V. For instance, the "quantum plane" xy=qyx gives rise to two different integrable systems: rational and trigonometric ones.
Cite
@article{arxiv.1906.07287,
title = {Determinants in Quantum Matrix Algebras and Integrable Systems},
author = {Dimitri Gurevich and Pavel Saponov},
journal= {arXiv preprint arXiv:1906.07287},
year = {2020}
}
Comments
Substantially revised version of the paper "Quantum determinant revisited"