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## Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results

Adamović, Dražen; Kac, Victor; Moseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren
Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results // Journal of algebra, 500 (2018), 117-152 doi:10.1016/j.jalgebra.2016.12.005 (podatak o recenziji nije dostupan, članak, znanstveni)

Naslov
Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results

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

Izvornik
Journal of algebra (0021-8693) 500 (2018); 117-152

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

Ključne riječi
Vertex algebra ; conformal vector ; Conformal embedding ; Conformal level ; Collapsing level

Sažetak
We find all values of $k\in \Bbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W- algebra $W_k( g, \theta)$ is conformal, where g is a basic simple Lie superalgebra and $-\theta$ its minimal root. In particular, it turns out that if $W_k(g, \theta)$ does not collapse to its affine part, then the possible values of these $k$ are either $-\frac{; ; ; ; ; ; 2}; ; ; ; ; ; {; ; ; ; ; ; 3}; ; ; ; ; ; h^\vee$ or $- \frac{; ; ; ; ; ; h^\vee- 1}; ; ; ; ; ; {; ; ; ; ; ; 2}; ; ; ; ; ;$, where $h^\vee$ is the dual Coxeter number of g for the normalization $(\theta, \theta)=2$. As an application of our results, we present a realization of simple affine vertex algebra $V_{; ; ; ; ; ; - \tfrac{; ; ; ; ; ; n+1}; ; ; ; ; ; {; ; ; ; ; ; 2}; ; ; ; ; ; }; ; ; ; ; ; (sl(n+1))$ inside the tensor product of the vertex algebra $W_{; ; ; ; ; ; \tfrac{; ; ; ; ; ; n-1}; ; ; ; ; ; {; ; ; ; ; ; 2}; ; ; ; ; ; }; ; ; ; ; ; (sl(2\vert n), \theta)$ (also called the Bershadsky-Knizhnik algebra) with a lattice vertex algebra.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
S.I. posvećen Efimu Zelmanovu povodom 60-og rođendana.

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

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, 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