By Cho-Ho Chu
Jordan concept has built quickly within the final 3 a long time, yet only a few books describe its various purposes. right here, the writer discusses a few contemporary advances of Jordan idea in differential geometry, advanced and useful research, through a variety of examples and concise ancient notes. those comprise: the relationship among Jordan and Lie conception through the Tits-Kantor-Koecher building of Lie algebras; a Jordan algebraic method of countless dimensional symmetric manifolds together with Riemannian symmetric areas; the one-to-one correspondence among bounded symmetric domain names and JB*-triples; and purposes of Jordan equipment in advanced functionality conception. the elemental constructions and a few practical analytic houses of JB*-triples also are mentioned. The booklet is a handy reference for specialists in advanced geometry or practical research, in addition to an creation to those parts for starting researchers. the new purposes of Jordan thought mentioned within the publication also needs to attract algebraists.