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

A notion of quantum matrix (QM-) algebra generalizes and unifies two famous families algebras from the theory groups: RTT-algebras reflection equation (RE-) algebras. These being generated by components a ‘quantum’ M possess certain properties which resemble structure theorems ordinary theory. It turns out that such results are naturally derived in more general framework QM-algebras. In this work we consider family Birman–Murakami–Wenzl (BMW) type defined with use R-matrix representations BMW Particular series include orthogonal symplectic types RTT- RE-algebras, as well their super-partners. For QM-algebras, investigate ‘characteristic subalgebras’ — subalgebras where coefficients characteristic polynomials take values. We define three sets generating elements subalgebra derive recursive Newton Wronski relations between them. also an associative ?-product for generators QM-algebra is proper generalization classical multiplication. determine set all ‘descendants’ M, prove ?-commutativity type.