Seminario di algebra e geometria
ore
14:15
presso Seminario II
In this series of seminars, I will give a gentle introduction to the differential
geometric and Lie algebraic aspects of supergravity.
I will first recall the description of supergravity theories in terms of Tanaka
structures (non-holonomic G-structures) on supermanifolds and elucidate
their relationship with a class of Z-graded Lie superalgebras
g = g_{-2}+ g_{-1} + g_0 +g_1+g_2
of depth two. I will then present some recent results, in collaboration with J.
Figueroa-O'Farrill (University of Edinburgh), on supergravity backgrounds
and the algebraic structure of Lie superalgebras generated by Killing spinors.
In the last part, I will recall the correspondence between different kinds
of 3-algebras that recently appeared in Chern-Simons theories and Z-graded
Lie superalgebras. The most general case is open and involves (generalized)
Kantor triple systems and Lie superalgebras of depth two.