Automorphisms of Regular Algebras

Details Automorphisms of Regular Algebras Automorphisms of Regular Algebras

2006-01-11

arxiv.org/abs/math/0601264v1

Mathematics

Quantum Algebra

8 pages, based on a talk at the International Workshop "Lie Theory and Its Applications in Physics VI" Varna, 2005

Scientific paper

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.

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