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Automorphisms of Regular Algebras

Todor Popov
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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.

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Todor Popov. 2006-01-11. Automorphisms of Regular Algebras. https://arxiv.org/abs/math/0601264

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