4 papers
Computation of cohomology of vertex algebras
Bojko Bakalov, Alberto De Sole, Victor G. Kac
We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical co…
p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)
Sylvain Carpentier, Alberto De Sole, Victor G. Kac +2
For each partition p of an integer N \geq 2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present…
Computation of cohomology of Lie conformal and Poisson vertex algebras
Bojko Bakalov, Alberto De Sole, Victor G. Kac
We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as f…
Local and non-local multiplicative Poisson vertex algebras and differential-difference equations
Alberto De Sole, Victor G. Kac, Daniele Valeri +1
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference H…