Generic super-orbits in [formula omitted] and their braided counterparts

Abstract

We introduce some braided varieties–braided orbits–by considering quotients of the so-called Reflection Equation Algebras associated with Hecke symmetries (i.e. special type solutions of the quantum Yang–Baxter equation). Such a braided variety is called regular if there exists a projective module on it, which is a counterpart of the cotangent bundle on a generic orbit O ∈ g l ( m ) ∗ in the framework of the Serre approach. We give a criterium of regularity of a braided orbit in terms of roots of the Cayley–Hamilton identity valid for the generating matrix of the Reflection Equation Algebra in question. By specializing our general construction we get super-orbits in g l ( m | n ) ∗ and a criterium of their regularity.