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Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)

Publications Mathématiques de l'IHÉS

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras...

Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type 𝐀 1

Bo Hou, Yanhong Guo (2015)

Czechoslovak Mathematical Journal

The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let Λ t be the Yoneda algebra of a reconstruction algebra of type 𝐀 1 over a field . I n t h i s p a p e r , a m i n i m a l p r o j e c t i v e b i m o d u l e r e s o l u t i o n o f t i s c o n s t r u c t e d , a n d t h e -dimensions of all Hochschild homology and cohomology groups of Λ t are calculated explicitly.

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang, Xueping Lei (2024)

Czechoslovak Mathematical Journal

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E , M be a Gorenstein projective A -module and B = End A M . We give an upper bound for the finitistic dimension of B in terms of homological data of M . Furthermore, if A is n -Gorenstein for 2 n < , then we show the global dimension of B is less than or equal to n plus the B -projective dimension of Hom A ( M , E ) . As an application, the global dimension of End A E is less than or equal to n .

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