Automorphisms of Regular Algebras
Abstract
Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin's construction can be extended for quantum spaces which are non-quadratic homogeneous algebras. Here given a regular Artin-Schelter algebra of dimension 3 we construct the quantum group of its symmetries, i.e., the Hopf algebra of its automorphisms. For quadratic Artin-Schelter algebras these quantum groups are contained in the the classification of the GL(3) quantum matrix groups due to Ewen and Ogievetsky. For cubic Artin-Schelter algebras we obtain new quantum groups which are automorphisms of cubic quantum spaces.
Cite
@article{arxiv.math/0601264,
title = {Automorphisms of Regular Algebras},
author = {Todor Popov},
journal= {arXiv preprint arXiv:math/0601264},
year = {2007}
}
Comments
8 pages, based on a talk at the International Workshop "Lie Theory and Its Applications in Physics VI" Varna, 2005