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A note on the affine vertex algebra associated to gl(1/1) at the critical level and its generalizations (CROSBI ID 246763)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Adamović, Dražen A note on the affine vertex algebra associated to gl(1/1) at the critical level and its generalizations // Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti, 532 (2017), 21; 76-88. doi: 10.21857/yrvgqtpk89

Podaci o odgovornosti

Adamović, Dražen

engleski

A note on the affine vertex algebra associated to gl(1/1) at the critical level and its generalizations

In this note we present an explicit realization of the affine vertex algebra V^cri(gl(1|1)) inside of the tensor product F ⊗ M where F is a fermionic verex algebra and M is a commutative vertex algebra. This immediately gives an alternative description of the center of V^cri(gl(1|1)) as a subalgebra M_0 of M. We reconstruct the Molev-Mukhin formula for the Hilbert-Poincare series of the center of V^cri(gl(1|1)). Moreover, we construct a family of irreducible Vcri(gl(1|1))-modules realized on F and parameterized by χ+, χ- ∈ C((z)). We propose a generalization of V^cri(gl(1|1)) as a critical level version of the super W_{;1+∞}; vertex algebra.

Vertex algebras ; affine Lie superalgebras ; critical level ; W-algebras

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Podaci o izdanju

532 (21)

2017.

76-88

objavljeno

1845-4100

1849-2215

10.21857/yrvgqtpk89

Povezanost rada

Matematika

Poveznice
Indeksiranost