Naslov
On logarithmic modules for affine vertex operator algebras

Autori
Adamović, Dražen

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
Seminar at School of Mathematical Sciences, Xiamen University

Mjesto i datum
Xiamen, Kina, 07.01.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Logarithmic modules ; affine vertex algebra

Sažetak
We shall first review basic results for logarithmic modules for vertex operator algebras and discuss methods for their constructions. Then we present recent explicit realizations of certain affine vertex algebras and discuss their applications in the representation theory. Admissible affine vertex operator algebras $V_{;k}; (\mathfrak g)$ are semi-simple in the category $\mathcal O$. In this talk, we shall consider $V_{;k}; (\mathfrak g)$--modules outside of the category $\mathcal O$. Logarithmic modules appear in the non-split extension of certain weight modules. Although $V_{;k}; (\mathfrak g)$--modules are modules for the affine Lie algebras, it is difficult to construct indecomposable and logarithmic modules using concepts from the representation theory of Lie algebras. We will show how these modules can be explicitly constructed using vertex-algebraic techniques. We also study a connection with triplet vertex algebras.

Izvorni jezik
Engleski

POVEZANOST RADA