Olivier Mathieu
Monday 9:30
Noetherianity of simple graded Lie algebras
Nicolás Andruskiewitsch
Monday 11:00
Pointed Hopf algebras of odd dimension and Nichols algebras over solvable groups
We classify finite-dimensional Nichols algebras of Yetter-Drinfeld modules with indecomposable support over finite solvable groups in characteristic 0, using a variety of methods including reduction to positive characteristic. As a consequence, all Nichols algebras over groups of odd order are of diagonal type, which allows us to describe all pointed Hopf algebras of odd dimension.
This is joint work with I. Heckenberger and L. Vendramin.
Vanessa Miemietz
Monday 13:30
Matt Westaway
Monday 15:00
Parabolic Induction of Losev-Premet Ideals
Parabolic induction is a fundamental tool within Lie theory which can be defined for many different Lie-theoretic objects; these include nilpotent orbits and their covers, ideals in universal enveloping algebras, representations of reduced enveloping algebras, and representations of finite W-algebras. This talk will introduce the notion of Losev-Premet ideals, which are related to each of the aforementioned objects in interesting ways. I will then explain some recent results regarding how they behave under parabolic induction. This talk will be based on joint work with S. Goodwin and L. Topley.
Lucas Buzaglo
Monday 16:30
Enveloping algebras of Lie algebras of derivations
Universal enveloping algebras of finite-dimensional Lie algebras are fundamental examples of well-behaved noncommutative rings, yet enveloping algebras of infinite-dimensional Lie algebras remain mysterious. For example, it is widely believed that they are never noetherian, but we are very far from being able to prove this in complete generality. In this talk, I will focus on my recent work with Jason Bell on the noetherianity of enveloping algebras of Lie algebras of derivations.
Oksana Yakimova
Tuesday 9:00
James Timmins
Tuesday 10:30
Augmented Iwasawa algebras of p-adic Lie groups
Representations of p-adic Lie groups are naturally modules over augmented Iwasawa algebras. These noncommutative rings are analogues of group algebras, and have a number of convenient properties, including the existence of a Gelfand-Kirillov type invariant. In this talk, I’ll explain all of the above, and demonstrate how ring-theoretic facts translate into theorems about modular representations.
Vincenzo di Bartolo
Tuesday 12:00
Injective and coherence dimension of augmented Iwasawa algebras
From a Mayer Vietoris presentation of the augmented Iwasawa algebra of SL_2(F) (and for other linear groups, with F a p-adic field) we are able to understand values of its injective dimension, and coherence dimension, a notion generalising Noetherianity.
Gwyn Bellamy
Tuesday 14:00
Filtered Koszul duality
In this talk I will revisit Koszul duality for filtered algebras U whose associated graded algebra A is Koszul. In this setting, duality is an equivalence between the derived category D(U) of U and the homotopy category of injective curved dg-modules for the Koszul dual algebra A!. Here the curvature element corresponds to the deformation data for U. Examples include the Weyl algebra, symplectic reflection algebras and deformed preprojective algebras. If there is time I will explain applications of this result, such as an explicit description of the “exotic” t-structure on the homotopy category of injective curved dg-modules one gets via this equivalence. This is based on joint work in progress with Simone Castellan and Isambard Goodbody.
Charles Conley
Tuesday 15:00
Annihilators of representations of vector field Lie algebras
A large class of irreducible admissible representations of Lie algebras of vector fields is given by the tensor field modules. We will discuss the 2-sided ideals in the universal enveloping algebra which annihilate these modules. We will focus on the algebra of vector fields on the line and the superalgebra of contact vector fields on the (1|1) superline. Time permitting, we will make some remarks on the case of the vector fields on the plane.
