Quantum matrix algebras of BMW type: Structure of the characteristic subalgebra

  title={Quantum matrix algebras of BMW type: Structure of the characteristic subalgebra},
  author={Oleg Ogievetsky and Pavel Pyatov},
  journal={Journal of Geometry and Physics},
2 Citations

Quantum doubles of Fock type and bosonization



Quantum matrix algebras of the GL(m|n) type: The structure and spectral parameterization of the characteristic subalgebra

We continue the study of quantum matrix algebras of the GL(m|n) type. We find three alternative forms of the Cayley-Hamilton identity; most importantly, this identity can be represented in a factored

Coideal subalgebras in quantum affine algebras

We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q -> 1 each subalgebra specializes to the


The general algebraic properties of the algebras of vector fields over the quantum linear groups GLq(N) and SLq(N) are studied. These quantum algebras appear to be quite similar to the classical

Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them

For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type

Quantum Groups

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions

A Ribbon Hopf Algebra Approach to the Irreducible Representations of Centralizer Algebras: The Brauer, Birman–Wenzl, and Type A Iwahori–Hecke Algebras

Abstract We show how the ribbon Hopf algebra structure on the Drinfel'd–Jimbo quantum groups of Types A, B, C, and D can be used to derive formulas giving explicit realizations of the irreducible

A guide to quantum groups

Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. Quasitriangular

Quantum groups and Yang-Baxter equations

The principles of the theory of quantum groups are reviewed from the point of view of the possibility of using them for deformations of symmetries in physics models. The R -matrix approach to the

Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras

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

Bicovariant quantum algebras and quantum Lie algebras

AbstractA bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun $$(\mathfrak{G}_q )$$ toUqg, given by elements of the pure