nLab magic supergravity







Magic Squares (MS’s), arrays of Lie algebras enjoying remarkable symmetry properties under reflection with respect to their main diagonal, were discovered long time ago by Freudenthal, Rozenfeld and Tits, and their structure and fascinating properties have been studied extensively in mathematics and mathematical physics, especially in relation to exceptional Lie algebras.

Following the seminal papers (Gunyadin-Sierra-Townsend 83, Gunyadin-Sierra-Townsend 83) magic squares have been related to the generalized electric-magnetic U-duality symmetries of particular classes of Maxwell-Einstein supergravity theories, called magic supergravities. In particular, non-compact, real forms of Lie algebras, corresponding to non-compact symmetries of (super)gravity theories, have become relevant as symmetries of the corresponding rank-3 simple Jordan algebras, defined over real normed division algebra (A=,,,𝕆)(A = \mathbb{R}, \mathbb{C}, \mathbb{H}, \mathbb{O}) or split (A=, S, S,𝕆 S)(A = \mathbb{R}, \mathbb{C}_S, \mathbb{H}_S, \mathbb{O}_S) composition algebras. Later on, some other MS’s have been constructed in literature through the exploitation of Tits’ formula.

(from Cacciatori-Cerchiai-Marrani 12)


Last revised on March 5, 2020 at 10:40:15. See the history of this page for a list of all contributions to it.