262 citations · 3.5k across the 155 of their papers we have counts for
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Classification of linearly compact simple rigid superalgebras
Nicoletta Cantarini, Victor G. Kac
The notion of an anti-commutative (resp. commutative) rigid superalgebra is a natural generalisation of the notion of a Lie (resp. Jordan) superalgebra. Intuitively rigidity means…
Classification of simple linearly compact n-Lie superalgebras
Nicoletta Cantarini, Victor G. Kac
We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n…
Poisson vertex algebras in the theory of Hamiltonian equations
Aliaa Barakat, Alberto De Sole, Victor G. Kac
We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian partial differential equations. Such an equation is c…
On complete reducibility for infinite-dimensional Lie algebras
M. Gorelik, V. Kac
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.