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

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

2005-11-25

arxiv.org/abs/math/0511618v1

Mathematics

Quantum Algebra

69 pages

Scientific paper

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.

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