2004/11/25 by Dimitri Gurevich, D. Gurevich, Pavel Saponov +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0411579
arxiv created 2004/11/25 · openalex publication_date 2004/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To some braiding R of Hecke type (a Hecke symmetry) we put into correspondence an associative algebra called the modified Reflection Equation Algebra (mREA). We construct a series of matrices L_(m), m=1,2,... with entries belonging to mREA such that each of them satisfies a version of the Cayley-Hamilton identity with central coefficients. We also consider some quotients of the mREA which are called the non-commutative orbits. For each of these orbits we construct a large family of projective modules. In this family we introduce an algebraic structure which is close to that of K0(\Fl(\Cn)). The algebraic structure respects an equivalence relation motivated by a "quantum" trace compatible with the initial Hecke symmetry R. For a subclass of non-commutative orbits we compute the spectrum of central elements of the mREA TrR(L_(m)k), k∈ \Bbb N.