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

Adamović, Dražen; Kac, Victor; Moseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
An application of collapsing levels to the representation theory of affine vertex algebras // International mathematics research notices (2018) doi:10.1093/imrn/rny237 (znanstveni, prihvaćen)

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

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
International mathematics research notices (2018)

Prihvaćen

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

Sažetak
We discover a large class of simple affine vertex algebras $V_{;k}; (\g)$, associated to basic Lie superalgebras $\g$ at non--admissible collapsing levels $k$, having exactly one irreducible $\g$--locally finite module in the category ${;\mathcal O};$. In the case when $\g$ is a Lie algebra, we prove a complete reducibility result for $V_k(\g)$-- modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra $V^k (\g)$ at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras $V_{;-1/2}; (C_n)$ and $V_{;-4};(E_7)$, we surprisingly obtain the realization of non- simple affine vertex algebras of types $B$ and $D$ having exactly one non-trivial ideal.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
HRZZ-IP-2013-11-2634 - Algebarske i kombinatorne metode u teoriji verteks algebri (Dražen Adamović, )
ZCI QuantiXLie

Ustanove
Prirodoslovno-matematički fakultet, Zagreb

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus