If R is a G-graded associative algebra, where G is an abelian group and β is a bicharacter for G, then R also has the structure of a Jordan color algebra. In addition, if R is endowed with a color involution ), then the symmetric elements S under ) are also a Jordan color algebra. Generalizing resul
Constructing Simple Lie Superalgebras from Associative Graded Algebras
β Scribed by S Montgomery
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 292 KB
- Volume
- 195
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
We consider the following problem: what is the most general Lie algebra or superalgebra satisfying a given set of Lie polynomial equations? The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of
The graded Lie algebra L associated to the Nottingham group is a loop algebra Γ΄f the Witt algebra W . The universal covering W of W has one-dimensional 1 1 1 Δentre, so that the corresponding loop algebra M of W has an infinite-dimen-1 Ε½ . Ε½ . sional centre Z M . As MrZ M is isomorphic to L, it foll
If α is a classical simple Lie superalgebra α / P n , the enveloping algebra Ε½ . Ε½ Ε½ .. U α is a prime ring and hence has a simple artinian ring of quotients Q U α by Ε½ Ε½ .. Goldie's Theorem. We show that if α has Type I then Q U α is a matrix ring Ε½ Ε½ .. Ε½ . over Q U α . On the other hand, if α s