PBW-deformations of \(N\)-Koszul algebras. (English) Zbl 1159.16026
Summary: For a quotient algebra \(U\) of the tensor algebra we give explicit conditions on its relations for \(U\) being a PBW-deformation of an \(N\)-Koszul algebra \(A\). We show that there is a one-to-one correspondence between such deformations and a class of \(A_\infty\)-structures on the Yoneda algebra \(\text{Ext}^*_A(k,k)\) of \(A\). We compute the PBW-deformations of the algebra whose relations are the anti-symmetrizers of degree \(N\) and also of cubic Artin-Schelter algebras.
MSC:
| 16S37 | Quadratic and Koszul algebras |
| 16S80 | Deformations of associative rings |
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
Keywords:
homogeneous algebras; Poincaré-Birkhoff-Witt deformations; \(N\)-Koszul algebras; tensor algebras; associated graded algebras; Yoneda algebras; Artin-Schelter algebrasReferences:
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