On simplicity of vacuum modules
M. Gorelik, V. Kac
TL;DR
This paper establishes criteria for the irreducibility of vacuum modules over affine Lie algebras and superalgebras, and derives simplicity conditions for minimal W-algebras, providing explicit formulas for certain cases.
Contribution
It provides necessary and sufficient conditions for vacuum module irreducibility and simplicity of minimal W-algebras, including explicit formulas for Virasoro and Neveu-Schwarz cases.
Findings
Criteria for irreducibility of vacuum modules
Conditions for simplicity of minimal W-algebras
Explicit vacuum determinant formulas for Virasoro and Neveu-Schwarz
Abstract
We find necessary and sufficient conditions of irreducibility of vacuum modules over affine Lie algebras and superalgebras. From this we derive conditions of simplicity of minimal W-algebras. Moreover, in the case of Virasoro and Neveu-Schwarz algebras we obtain explicit formulas for vacuum determinants.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons