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

Autori
Adamović, Dražen

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 532 (2017), 21; 76-88

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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