Generic super-orbits in gl(m|n)* and their braided counterparts
Quantum Algebra
2015-05-18 v1
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 in 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)* and a criterium of their regularity.
Keywords
Cite
@article{arxiv.1002.1592,
title = {Generic super-orbits in gl(m|n)* and their braided counterparts},
author = {D. I. Gurevich and P. A. Saponov},
journal= {arXiv preprint arXiv:1002.1592},
year = {2015}
}