Generic super-orbits in gl(m|n)∗gl(m|n)∗ and their braided counterparts

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∈gl(m)∗O∈gl(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 gl(m|n)∗gl(m|n)∗ and a criterium of their regularity.