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Determinants in quantum matrix algebras and integrable systems.

Authors :
Gurevich, D. I.
Saponov, P. A.
Source :
Theoretical & Mathematical Physics. May2021, Vol. 207 Issue 2, p626-639. 14p.
Publication Year :
2021

Abstract

We define quantum determinants in quantum matrix algebras related to pairs of compatible braidings. We establish relations between these determinants and the so-called column and row determinants, which are often used in the theory of integrable systems. We also generalize the quantum integrable spin systems using generalized Yangians related to pairs of compatible braidings. We demonstrate that such quantum integrable spin systems are not uniquely determined by the "quantum coordinate ring" of the basic space . For example, the "quantum plane" yields two different integrable systems: rational and trigonometric. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00405779
Volume :
207
Issue :
2
Database :
Academic Search Index
Journal :
Theoretical & Mathematical Physics
Publication Type :
Academic Journal
Accession number :
151935204
Full Text :
https://doi.org/10.1134/S004057792105007X