Geometry of non-commutative orbits related to Hecke symmetries

Abstract

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 $K^0(\Fl(\C^n))$. 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 Tr_R(L_(m)^k), k\in {\Bbb N}.

References in corpus (1)

• Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory

Cited by in corpus (6)

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• Quantization of Physical Models and Non-Commutative Geometry
• Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type
• Quantization of orbit bundles in $g{l}^{\ast }(n,C)$