Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras

1999/12/24 by A. P. Isaev, Isaev, A. P., O. Ogievetsky +5 · 3 citations
Mathematics · Physics and Astronomy · #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/9912197

11 pages, LaTeX. Submitted to the Proceedings of the Intern. Seminar "Supersymmetries and Quantum Symmetries" (27-31 July, 1999, Dubna, Russia)

arxiv created 1999/12/24 · openalex publication_date 1999/12/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the framework of the Drinfeld theory of twists in Hopf algebras we construct quantum matrix algebras which generalize the Reflection Equation and the RTT algebras. Finite-dimensional representations of these algebras related to the theory of nonultralocal spin chains are presented. The Cayley-Hamilton-Newton identities are demonstrated. These identities allow to define the quantum spectrum for the quantum matrices. We mention possible applications of the new quantum matrix algebras to constructions of noncommutative analogs of Minkowski space and quantum Poincaré algebras.

Cited by

• Cayley--Hamilton Theorem for Orthogonal Quantum Matrix Algebras
• Reciprocal relations for orthogonal quantum matrices
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization

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