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Lie isomorphisms of the skew elements of a simple ring with involution

✍ Scribed by Wallace S Martindale III

Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
508 KB
Volume
36
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

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Let R be a prime ring with involution of the first kind, and characteristic / 2, 3. Let K denote the skew elements of R, and let C denote the extended centroid of Ε½ . R . Assume that RC : C / 1, 4, 16. It is shown that any Lie derivation of K into Β² : itself can be extended to an ordinary derivation

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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

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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

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## dedicated to helmut wielandt on the occasion of his 90th birthday Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t ∼ = H. In this