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Primeness of the enveloping algebra of the special Lie superalgebras

โœ Scribed by Mark C. Wilson; Geoffrey Pritchard

Publisher
Springer
Year
1998
Tongue
English
Weight
189 KB
Volume
70
Category
Article
ISSN
0003-889X

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๐Ÿ“œ SIMILAR VOLUMES

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We write det L L / 0 q y y if the matrix formed by brackets between elements of a basis of L L is nonsinguy lar. Unlike Lie super algebras, a Lie color algebra L L may have det L L / 0 and a ลฝ . universal enveloping algebra U L L which is not prime. We will provide examples ลฝ . and show that U L L i

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If แ’„ is a classical simple Lie superalgebra แ’„ / P n , the enveloping algebra ลฝ . ลฝ ลฝ .. U แ’„ is a prime ring and hence has a simple artinian ring of quotients Q U แ’„ by ลฝ ลฝ .. Goldie's Theorem. We show that if แ’„ has Type I then Q U แ’„ is a matrix ring ลฝ ลฝ .. ลฝ . over Q U แ’„ . On the other hand, if แ’„ s