%0 Journal Article
%T A note on the affine vertex algebra associated to gl(1|1) at the critical level and its generalizations
%A Adamovi£¿
%A Dra£¿en
%J -
%D 2017
%R 10.21857/yrvgqtpk89
%X Sa£¿etak 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 ¦Ö+, ¦Ö- ¡Ê C((z)). We propose a generalization of V^cri(gl(1|1)) as a critical level version of the super W_{1+¡Þ} vertex algebra
%K Vertex algebras
%K affine Lie superalgebras
%K critical level
%K W-algebras
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=274959