Algebra Commons^™

Invariant Nonassociative Algebra Structures On Irreducible Representations Of Simple Lie Algebras, Murray Bremner, Irvin R. Hentzel

Irvin Roy Hentzel

An irreducible representation of a simple Lie algebra can be a direct summand of its own tensor square. In this case, the representation admits a nonassociative algebra structure which is invariant in the sense that the Lie algebra acts as derivations. We study this situation for the Lie algebra sl(2).