# Algebra Seminar: Integrable representation of full toroidal Lie algebras

- Date: 21 March 2023, 15:15–17:00
- Location: Ångström Laboratory, Å64119
- Type: Seminar
- Lecturer: Santanu Tantubay (Harish-Chandra Research Institute, Allahabad)
- Organiser: Matematiska institutionen
- Contact person: Volodymyr Mazorchuk

Welcome to this seminar held by Santanu Tantubay (Harish-Chandra Research Institute, Allahabad) with the title "Integrable representation of full toroidal Lie algebras".

Participate on site or via Zoom link (meeting ID: 645 5572 6999, for passcode: please contact the organizer).

**Abstract:** Rational quantum torus is a non-commutative analogue of Laurent polynomial ring. Toroidal algebra is an n-variable generalization of affine Kac-Moody algebra.

The full toroidal algebra is a Lie algebra which contains toroidal algebra as a subalgebra. Integrable representations of affine Kac-Moody algebra, toroidal algebra and full toroidal algebra are well studied by several mathematicians.

In the first part of the talk, we shall discuss about construction of rational quantum torus, derivation space of rational quantum torus, toroidal Lie algebra and full toroidal Lie algebras. Then we will discuss about root space decomposition of toroidal algebra and full toroidal algebra.

In the second part of the talk we will see the construction of full toroidal Lie algebra over rational quantum torus and its root space decomposition. Then we will show that any integrable simple module with finite dimensional weight spaces is a highest weight module and we will discuss the highest weight space in detail.

This is a seminar in our algebra seminar series.