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On the Goldie Quotient Ring of the Enveloping Algebra of a Classical Simple Lie Superalgebra

✍ Scribed by Ian M Musson

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
100 KB
Volume
235
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 osp 1, 2 r then by extending the center 0 Ε½ . of U α’„ we obtain a prime ring whose Goldie quotient ring is a matrix ring over the quotient division ring of a Weyl algebra. This is an analog of a result of Gelfand and Kirillov.

πŸ“œ SIMILAR VOLUMES

On the Lie Structure of the Skew Element
On the Lie Structure of the Skew Elements of a Simple Superalgebra with Superinvolution
✍ Carlos GΓ³mez-Ambrosi; Ivan P. Shestakov πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 321 KB

We investigate the Lie structure of the Lie superalgebra K of skew elements of a unital simple associative superalgebra A with superinvolution over a field of characteristic not 2. It is proved that if A is more than 16-dimensional over its w x center Z, then any Lie ideal U of K satisfies either U