August 2020 – QuantiXLie

Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels

27/08/2020 Rafael Mrđen 0

Authors: Dražen Adamović, Ana Kontrec Journal of Algebra and its applications (2020), https://doi.org/10.1142/S0219498821501024 Abstract: We study the representation theory of the Bershadsky-Polyakov algebra . In particular, Zhu algebra of is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category for the Bershadsky-Polyakov algebra […]

On Zhu’s algebra and $C_2$ –algebra for symplectic fermion vertex algebra $SF(d)^+$

27/08/2020 Rafael Mrđen 0

Authors: Dražen Adamović, Ante Čeperić Journal of Algebra, Volume 563, 1 December 2020, Pages 376-403, https://doi.org/10.1016/j.jalgebra.2020.07.019 Abstract: In this paper, we study the family of vertex operator algebras , known as symplectic fermions. This family is of a particular interest because these VOAs are irrational and -cofinite. We determine Zhu’s algebra and show that the equality of dimensions of and the -algebra holds for d≥2 (the […]

A note on principal subspaces of the affine Lie algebras in types $B_l^{(1)}, C_l^{(1)}, F_4^{(1)}$ and $G_2^{(1)}$

27/08/2020 Rafael Mrđen 0

Author: Marijana Butorac Communications in Algebra, doi: 10.1080/00927872.2020.1788046 Abstract: We construct quasi-particle bases of principal subspaces of standard modules , where , and denotes the fundamental weight of affine Lie algebras of type , or of level one. From the given bases we find characters of principal subspaces. Keywords: Affine Lie algebras, combinatorial bases, principal subspaces, quasi-particles, vertex operator algebras