Higher symplectic reflection algebras and non-homogeneous N-Koszul property
By R. Berger, V. Ginzburg. 2005
57 citations recorded by the source corpus.
Abstract We study a class of associative algebras associated to finite groups acting on a vector space. These algebras are non-homogeneous N-Koszul algebra generalizations of symplectic reflection algebras [P. Etingof, V. Ginzburg, Symplectic reflection algebras, Calogero–Moser space, and deformed Harish-Chandra homomorphism, Invent. Math. 147 (2002) 243–348]. The Koszul property was generalized to homogeneous algebras of degree N > 2 in [R. Berger, Koszulity for nonquadratic algebras, J. Algebra 239 (2001) 705–734]. In the present paper, the extension of the Koszul property to non-homogeneous algebras is realized through a PBW theorem. This PBW theorem is the generalization to the N-case of a quadratic result obtained by Braverman and Gaitsgory [A. Braverman, D. Gaitsgory, Poincare–Birkhoff–Witt theorem for quadratic algebras of Koszul type, J. Algebra 181 (1996) 315–328] (see also [A. Polishchuk, L. Positselski, Quadratic Algebras, Univ. Lecture Ser., vol. 37, Amer. Math. Soc., Providence, RI, 2005]). We work in the general setting where the ground ring is an arbitrary von Neumann regular ring.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d512fe1389d9546bea9e8c39b7dfd74ae1021f17
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Citations in the corpus
- Generalizing the notion of Koszul algebra (2007, background): “Purity then becomes a powerful homological tool, see for example [4] or [8].”
- Poincaré-Birkhoff-Witt deformations of Calabi-Yau algebras (2006, background): “Hochschild cohomology, deformations of algebras, Calabi–Yau algebras, quiver algebras.”