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Classical and variational Poisson cohomology
Bojko Bakalov, Alberto De Sole, Reimundo Heluani +2
We prove that, for a Poisson vertex algebra V, the canonical injective homomorphism of the variational cohomology of V to its classical cohomology is an isomorphism, provided that…
An operadic approach to vertex algebra and Poisson vertex algebra cohomology
Bojko Bakalov, Alberto De Sole, Reimundo Heluani +1
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomo…
A Lax type operator for quantum finite W-algebras
Alberto De Sole, Victor Kac, Daniele Valeri
For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite…
Finite W-algebras for gl_N
Alberto De Sole, Victor G. Kac, Daniele Valeri
We study the quantum finite W-algebras W(gl_N,f), associated to the Lie algebra gl_N, and its arbitrary nilpotent element f. We construct for such an algebra an r_1 x r_1 matrix L(…