Victor G. Kac
Massachusetts Institute of Technology
389 Papers
2.3K Citations
Victor G. Kac is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Lie conformal algebra & Lie algebra. The author has an hindex of 73, co-authored 373 publications. Previous affiliations of Victor G. Kac include Institute for Advanced Study & Institut des Hautes Études Scientifiques.
Chat about Author
Papers
Freely Generated Vertex Algebras and Non–Linear Lie Conformal Algebras
Alberto De Sole,Victor G. Kac +1 more
TL;DR: In this paper, the notion of a nonlinear Lie conformal superalgebra was introduced and a PBW theorem for its universal enveloping vertex algebra was proved. But the problem of classification of finitely generated simple graded vertex algebras was not addressed.
Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
TL;DR: In this article, the authors provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algesbras and establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.
Classification of linearly compact simple Nambu-Poisson algebras
TL;DR: In this article, the notion of universal odd generalized Poisson superalgebra associated with an associative algebra A was introduced and a complete classification of simple linearly compact n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero was given.
Representations of the exceptional lie superalgebra E(3, 6) I: Degeneracy conditions
Victor G. Kac,Alexei Rudakov +1 more
TL;DR: In this article, the authors obtained a classification of simple infinite dimensional Lie superalgebras of vector fields which extends the well known classification of E. Cartan in the Lie algebra case.
•Posted Content
A Lax type operator for quantum finite W-algebras
TL;DR: For a reductive Lie algebra g, its nilpotent element f and its faithful finite dimensional representation, a Lax operator L(z) with coefficients in the quantum finite W-algebra W(g, f) was constructed in this paper.