The Kac Construction of the Centre of for Lie Superalgebras
By M. Gorelik. 2004
47 citations recorded by the source corpus.
Abstract In 1984, Victor Kac [8] suggested an approach to a description of central elements of a completion of for any Kac-Moody Lie algebra . The method is based on a recursive procedure. Each step is reduced to a system of linear equations over a certain subalgebra of meromorphic functions on the Cartan subalgebra. The determinant of the system coincides with the Shapovalov determinant for . We prove that the Kac approach can also be applied to finite dimensional Lie superalgebras with Cartan matrix A (as claimed in [8]) and reproduce for them Sergeev’s description of the centers of [14]. In order to prove this, one needs to show that the recursive procedure stops after a finite number of steps. The original paper [8] does not indicate how to check this fact. Here we give a detailed presentation of the Kac approach and apply it to finite dimensional Lie superalgebras . In particular, we deduce the Kac formulas for the Shapovalov determinants and verify the finiteness of the recursive procedure.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c1917f69cda16bc42497f019ee1bea1f8af51c6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- ON ASSOCIATED VARIETY FOR LIE SUPERALGEBRAS (2005, background): “Easily follows from the description of the Z formulated in [12] and proven [4] and in [9].”