Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras

Details Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras

1999-12-24

arxiv.org/abs/math/9912197v1

Mathematics

Quantum Algebra

11 pages, LaTeX. Submitted to the Proceedings of the Intern. Seminar "Supersymmetries and Quantum Symmetries" (27-31 July, 199

Scientific paper

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 Poincar\'e algebras.

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