Hecke symmetries and characteristic relations on Reflection Equation algebras

TL;DR

This paper explores how Hecke symmetries shape the algebraic structure of Reflection Equation algebras, deriving analogues of classical matrix relations like Newton and Cayley-Hamilton theorems for these quantum algebras.

Contribution

It introduces new algebraic relations for RE algebras associated with finite rank even Hecke symmetries, extending classical matrix theory into quantum algebra context.

Findings

Derived Newton relations for RE algebras

Established Cayley-Hamilton theorem analogues

Analyzed influence of Hecke symmetry properties

Abstract

We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived.