Seminar for Algebra, SCE QuantiXLie

On Tuesday, February 28, 2023, 15:00 hours, Lucia Bagnoli will hold lecture as part of Seminar for Algebra titled:

“Finite irreducible modules over some conformal superalgebras”.

Lecture will be held in lecture room A101, Department of Mathematics.

All Seminar members and others interested are invited.

Abstract: In this talk we recall the definition and main properties of conformal superalgebras. Then we present the classification of the finite irreducible modules over the conformal superalgebra K'_4 obtained by their correspondence with finite conformal modules over the associated annihilation superalgebra A(K'_4). This is achieved by a complete classification of singular vectors in generalized Verma modules for A(K'_4). We also show that morphisms between generalized Verma modules can be arranged in infinitely many bilateral complexes. This classification is a joint work with F. Caselli.

Then we present a result on the homology of these complexes that provides an explicit realization of all irreducible quotients.