Metrised algebras and applications

by Prof. Vladimir Tkatjev (LiU Maths department)

Friday 26 Jan 2024, 13:00 → 14:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

Abstract. Jordan algebras were invented in 1930s by Jordan, von Neuman and Wigner in a hope to generalize the orthodox formulation of quantum mechanics. As remarked by Kevin McCrimmon, "if you open up a Lie algebra and look inside, 9 times out of 10 there is a Jordan algebra (of pair) which makes it work”.

Jordan algebras are only one of several interesting (and very related) classes of commutative nonassociative algebras appearing unexpectedly in different areas of physics and mathematics, including black hole physics, exotic viscosity solutions to nonlinear PDEs and mean curvature hypercones. In my talk, I will give a short friendly introduction into the subject with focus on metrized algebras and the Peirce decomposition toolkit.