Title: Killing Metrized Exact Commutative Algebras
Speaker: Daniel Fox
Institution: Universidad Politécnica de Madrid
Date & Time: September 5, 2024, 20:00–22:00
Location: Zoom ID: 904 645 6677, Password: 2024
A commutative algebra is
exact if the traces of its multiplication endomorphisms vanish and
Killing metrized if its Killing-type trace-form is invariant. These algebras are neither unital nor associative, forming a class that may appear either overly specialized or too broad to analyze. Examples include deunitalizations of étale associative algebras, semisimple Jordan algebras, tensor products of semisimple Lie algebras, Griess algebras of certain vertex operator algebras, and algebras linked to combinatorial structures like Steiner triple systems.
The talk motivates the study of Killing metrized exact commutative algebras and introduces constructions based on an analogy between connection curvature and the algebra’s associator, which organizes their analysis. These tools are used to classify such algebras over general fields in dimensions up to four and identify subclasses amenable to further study.
Daniel Fox is a Professor of Mathematics at the Universidad Politécnica de Madrid, Spain. His research focuses on non-associative algebras, Lie theory, and their applications to mathematical physics and combinatorics.
