Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras

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.

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

References in corpus (4)

• Extended jordanian twists for Lie algebras
• Quantum and Braided Linear Algebra
• Quantum groups and deformed special relativity
• Twist-related geometries on q-Minkowski space

Cited by in corpus (5)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them
• Cayley-Hamilton theorem for quantum matrix algebras of GL(m|n) type
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
• Cayley-Hamilton Theorem for Symplectic Quantum Matrix Algebras