Back to Search
Start Over
Classification of quadratic and cubic PBW algebras on three generators
- Publication Year :
- 2018
-
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 Gr\"obner 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.<br />Comment: 79 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1806.06844
- Document Type :
- Working Paper