Enveloping algebras of Slodowy slices and Goldie rank
✍ Scribed by Alexander Premet
- Publisher
- SP Birkhäuser Verlag Boston
- Year
- 2011
- Tongue
- English
- Weight
- 681 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1083-4362
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let G be a simple, simply connected algebraic group over C; g ¼ Lie G; NðgÞ the nilpotent cone of g; and ðE; H; F Þ an sl 2 -triple in g: Let S ¼ E þ Ker ad F ; the special transverse slice to the adjoint orbit O of E; and S 0 ¼ S \ NðgÞ: The coordinate ring C½S 0 is naturally graded (See Slodowy, '
If ᒄ is a classical simple Lie superalgebra ᒄ / P n , the enveloping algebra Ž . Ž Ž .. U ᒄ is a prime ring and hence has a simple artinian ring of quotients Q U ᒄ by Ž Ž .. Goldie's Theorem. We show that if ᒄ has Type I then Q U ᒄ is a matrix ring Ž Ž .. Ž . over Q U ᒄ . On the other hand, if ᒄ s