Classification of quadratic and cubic PBW algebras on three generators

Abstract

We give a complete classification of quadratic algebras A, with Hilbert series $H_A=(1-t{)}^{-3}$, which is the Hilbert series of commutative polynomials on 3 variables. Koszul algebras as well as algebras with quadratic Gröbner basis among them are identified. We also give a complete classification of cubic algebras A with Hilbert series $H_A=(1+t{)}^{-1}(1-t{)}^{-3}$. These two classes of algebras contain all Artin-Schelter regular algebras of global dimension 3. As far as the latter are concerned, our results extend well-known results of Artin and Schelter by providing a classification up to an algebra isomorphism.

79 pages

References in corpus (2)

• Calabi-Yau algebras
• Potential algebras with few generators

Cited by in corpus (4)

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