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Quantum algebra of multiparameter Manin matrices.
- Source :
-
Journal of Algebra . Oct2024, Vol. 655, p586-618. 33p. - Publication Year :
- 2024
-
Abstract
- Multiparametric quantum semigroups M q ˆ , p ˆ (n) are generalization of the one-parameter general linear semigroups M q (n) , where q ˆ = (q i j) and p ˆ = (p i j) are 2 n 2 parameters satisfying certain conditions. In this paper, we study the algebra of multiparametric Manin matrices using the R-matrix method. The systematic approach enables us to obtain several classical identities such as Muir's identities, Newton's identities, Capelli-type identities, Cauchy-Binet's identity both for determinant and permanent as well as a rigorous proof of the MacMahon master equation for the quantum algebra of multiparametric Manin matrices. Some of the generalized identities are also lifted to multiparameter q -Yangians. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 655
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 177880743
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2023.06.002