Invariant Nonassociative Algebra Structures on Irreducible Representations of Simple Lie Algebras
Bremner, Murray ; Hentzel, Irvin
Experiment. Math., Tome 13 (2004) no. 1, p. 231-256 / Harvested from Project Euclid
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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 {\small $sl(2)$}.
Publié le : 2004-05-14
Classification:  Simple Lie algebras,  representations,  anticommutative algebras,  polynomial identities,  computational linear algebra,  17-04,  17A30,  17B60,  17-08,  17A36,  17B10,  17D10 
@article{1090350937,
     author = {Bremner, Murray and Hentzel, Irvin},
     title = {Invariant Nonassociative Algebra Structures on Irreducible Representations of Simple Lie Algebras},
     journal = {Experiment. Math.},
     volume = {13},
     number = {1},
     year = {2004},
     pages = { 231-256},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1090350937}
}

Bremner, Murray; Hentzel, Irvin. Invariant Nonassociative Algebra Structures on Irreducible Representations of Simple Lie Algebras. Experiment. Math., Tome 13 (2004) no. 1, pp.  231-256. http://gdmltest.u-ga.fr/item/1090350937/