10 citations · 30 across the 5 of their papers we have counts for
6 papers
Conformal operads and the basic vertex algebra cohomology complex
Alberto De Sole, Reimundo Heluani, Victor Kac
We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and…
Integrable triples in semisimple Lie algebras
Alberto De Sole, Mamuka Jibladze, Victor G. Kac +1
We classify all integrable triples in simple Lie algebras, up to equivalence. The importance of this problem stems from the fact that for each such equivalence class one can constr…
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…