Dept Math & Stat UiT, Forskningsparken B459 & Zoom
4-11 Oct 2021 Mon 14:00-15:30
Francesco Toppan (Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro)
"Signatures of nonassociativity from the octonionic description of exceptional Lie (super)algebras"
In this series of two talks I point out that the octonionic structure constants play a dual role. On one side they define the nonassociativity of the octonionic multiplication; on the other side they define covariant forms and invariant traces which can be used to identify “signatures of nonassociativity” which manifest themselves as exceptional algebraic structures.
I illustrate, as a specific example, the construction of superconformal quantum mechanics with exceptional F(4) and G(3) spectrum-generating superalgebras. The duality, on the other hand, has far reaching consequences and the method has a wider range of applications.
The motivations behind this investigation lies on the fact that the nonassociative division algebra of the octonions is the unifying feature behind several exceptional mathematical structures: the 5 exceptional Lie algebras, the 2 exceptional superalgebras G(3) and F(4), the exceptional Albert algebra, etc.
In physics, octonions nicely describe unique structures like the 10-dimensional superstring theory, the 11-dimensional supergravity and the M-theory. I will present several motivations to exploit the duality of octonionic structure constants from pure mathematics, to fundamental and applied physics.
(To join Zoom: please contact Boris Kruglikov.)