Graded Lie algebras defined by Jordan algebras and their representations

Details Graded Lie algebras defined by Jordan algebras and their representations Graded Lie algebras defined by Jordan algebras and their representations

2004-12-09

arxiv.org/abs/math/0412186v2

Mathematics

Representation Theory

7 pages; MSC numbers updated

Scientific paper

We introduce the notion of a generalized representation of a Jordan algebra with unit. The greneralized representation has the following properties: (1) Usual representations and Jacobson representations correspond to special cases of generalized representations. (2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. (3) There is a one-to-one correspondence between irreducible generalized representations of a Jordan algebra A and irreducible representations of a graded Lie algebra L(A)=U_{-1}\oplus U_0\oplus U_1 corresponding to A (the Lie algebra L(A) coincides with the TKK construction when A has a unit). The latter correspondence allows to use the theory of representations of Lie algebras to study generalized representations of Jordan algebras. In particular, one can classify irreducible generalized representations of semisimple Jordan algebras and also obtain classical results about usual representations and Jacobson representations in a simple way.

Affiliated with

Also associated with

No associations

Rating

Graded Lie algebras defined by Jordan algebras and their representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Graded Lie algebras defined by Jordan algebras and their representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graded Lie algebras defined by Jordan algebras and their representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-152288