Naslov
Smith algebra and classification of irreducible modules for certain W-algebras

Autori
Kontrec, Ana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Representation Theory XVI

Mjesto i datum
Dubrovnik, Hrvatska, 24.06.2019. - 29.06.2019

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Vertex algebra ; W-algebras ; Bershadsky–Polyakov algebra ; Zhu’s algebra

Sažetak
We want to study the representation theory of some irrational affine W-algebras (joint project with D. Adamovic). In this talk, we study representations of Bershadsky-Polyakov algebra $W^k(sl_3, f_{; ; \theta}; ; )$, the minimal affine W-algebra associated to $sl_3$ at level k=-5/3, using two approaches: one which relies on number theoretical methods and another one which is based on the highest weight theory for modules of the Smith associative algebra. In particular, Zhu algebra of $W_k(sl_3, f_{; ; \theta}; ; )$ is realized as a quotient of the Smith algebra. We investigate this connection and use it to classify irreducible ordinary modules.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA