Naslov
An application of collapsing levels to the representation theory of affine vertex algebras

Autori
Adamović, Dražen ; Kac, Victor ; Moseneder Frajria, Pierluigi ; Papi, Paolo ; Perše, Ozren

Izvornik
International mathematics research notices (1073-7928) 2020 (2018), 13; 4103-4143

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

Ključne riječi
affine vertex algebra ; W-algebra ; complete reducibility

Sažetak
We discover a large class of simple affine vertex algebras Vk(g)⁠, associated to basic Lie superalgebras g at non-admissible collapsing levels k⁠, having exactly one irreducible g-locally finite module in the category O⁠. In the case when g is a Lie algebra, we prove a complete reducibility result for Vk(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra Vk(g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V−1/2(Cn) and V−4(E7)⁠, we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA