14:00
Searching for 3-dimensional subalgebras
Abstract
Let g be the Lie algebra of a simple algebraic group over an algebraically closed field of characteristic p. When p=0 the celebrated Jacobson-Morozov Theorem promises that every non-zero nilpotent element of g is contained in a simple 3-dimensional subalgebra of g (an sl2). This has been extended to odd primes but what about p=2? There is still a unique 3-dimensional simple Lie algebra, known colloquially as fake sl2, but there are other very sensible candidates like sl2 and pgl2. In this talk, Adam Thomas from the University of Warwick will discuss recent joint work with David Stewart (Manchester) determining which nilpotent elements of g live in subalgebras isomorphic to one of these three Lie algebras. There will be an abundance of concrete examples, calculations with small matrices and even some combinatorics.
We are pleased to announce that the Graduate School researcher training programme for Michaelmas term has now been finalised and is open for booking. Sessions are available free of charge to postgraduate students across the University. All training sessions are offered in hybrid format and can be joined either in person in the Graduate School Room in Rewley House (Wellington Square) or online through Teams.
Decimitry Sciences is a UK–US company headquartered in Oxford, specialising in causal reasoning for enterprises, irrespective of data quality. Its technology merges causal inference, multidimensional data processing, predictive analysis, and novel mathematical models to deliver adaptive, human-level decision-making, even when data is limited or mostly nonexistent.
15:00