Naslov
On indecomposable and logarithmic modules for affine vertex operator algebras

Autori
Adamović, Dražen

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

Skup
Mini-workshop on algebraic structures in CFT

Mjesto i datum
Utrecht, Nizozemska, 19.09.2018

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
indecomposable modules, logarithmic modules, affine vertex algebras

Sažetak
In the first part of the talk we review our 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 will also show that certain Whittaker modules are also weak $V_{; ; k}; ; (\mathfrak g)$--modules.

Izvorni jezik
Hrvatski

Znanstvena područja
Matematika

POVEZANOST RADA