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

Abstract

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 QM-algebras, we investigate a structure of its characteristic subalgebra (the subalgebra in which the coefficients of characteristic polynomials take values). We define 3 sets of generating elements of the characteristic subalgebra and derive recursive Newton and Wronski relations between them. For the family of the orthogonal type QM-algebras, additional reciprocal relations for the generators of the characteristic subalgebra are obtained.

69 pages

References in corpus (4)

• Cayley-Hamilton theorem for quantum matrix algebras of GL(m|n) type
• Geometry of non-commutative orbits related to Hecke symmetries
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
• Quantum conjugacy classes of simple matrix groups

Cited by in corpus (10)

• Spectral extension of the quantum group cotangent bundle
• Braids, Shuffles and Symmetrizers
• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization
• Spectral parameterization for the power sums of quantum supermatrix
• Cayley-Hamilton Theorem for Symplectic Quantum Matrix Algebras
• Braidings of Tensor Spaces
• q-Pascal's triangle and irreducible representations of the braid group B_3 in arbitrary dimension
• Representations of quantum conjugacy classes of orthosymplectic groups
• Representations of the braid group B_n and the highest weight modules of U(sl_{n-1}) and U_q(sl_{n-1})
• The Dzhumadildaev brackets: a hidden supersymmetry of commutators and the Amitsur-Levitzki-type identities