U utorak 10. studenoga 2026. od 15 do 18 sati , u predavaonici A102 , u okviru Seminara za algebru održat će se istraživačka radionica iz verteks-algebri uz financijsku potporu
- HRZZ projekta IP-2022-10-9006 „Afine vertex algebre i W-algebre” ,
- Znanstvenog centra izvrsnosti QuantiXLie.
Na radionici će se diskutirati o teoriji konformnih i kolapsirajućih nivoa afinih verteks-algebri i W-algebri, a prigodna motivacijska predavanja održat će Pierluigi Möseneder Frajria i Paolo Papi prema sljedećem rasporedu:
15:00–16:00 — Pierluigi Möseneder Frajria, Politecnico di Milano
Conformal and collapsing levels (I)
Sazetak: An embedding of a vertex operator algebra V into another vertex operator algebra V' is said to be conformal if it maps the conformal vector of V onto the conformal vector of V'. Let g be a simple Lie algebra or a basic classical Lie superalgebra and f a nilpotent element. If k is a noncritical complex number, let W_k(g,f) be the simple W-algebra attached to f via BRST cohomology. The level k is said to be conformal if the affine vertex subalgebra generated by the currents of W_k(g,f) embeds conformally in W_k(g,f). The level is said to be collapsing if this affine vertex subalgebra coincides with W_k(g,f). The determination of conformal and collapsing levels is relevant as it leads in many cases to the discovery of interesting phenomena. We will review the development of this study from early work of physicists to very recent results.
16:00–17:00 — Paolo Papi, Sapienza Università di Roma
Conformal and collapsing levels (II)
Sazetak: This talk builds on the content of the previous talk. Given a basic Lie superalgebra g, a nilpotent element f and a level k, consider the simple affine W-algebra W_k(g,f). I will present a simple criterion for a homomorphism from an affine vertex algebra into a vertex operator superalgebra to be conformal, together with an additional condition guaranteeing that it is surjective onto the simple quotient. For W-algebras, all the conditions can be read off from the decomposition of g under the centralizer of the sl(2)-triple and the triple itself. The key condition is that the adjoint representation of sl(2), tensored with the trivial representation of the centralizer, occurs in g exactly once. This refines earlier criteria of Adamović, Möseneder Frajria and the speaker, and extends our results on hook-type and rectangular W-algebras. We determine all the cases covered by the criterion in the classical types and obtain the complete list of collapsing levels for G2. We also find many new collapsing levels at non-admissible levels. These results give new quasi-lisse W-algebras and conjectures on associated varieties. Finally, I will discuss the Griess algebra carried by the weight-two subspace of the affine coset, and the emergence of multiple Virasoro elements.
This is joint work with D. Adamović, T. Arakawa, T. Creutzig, A. Linshaw, A. Moreau and P. Möseneder Frajria.
17:00-18:00 Diskusija
Pozivaju se članovi Seminara i svi zainteresirani da prisustvuju ovoj istraživačkoj radionici.
Pristupačnost
