Little jordan clofford algebras
作者:
Kevin McCrimmon,
期刊:
Communications in Algebra
(Taylor Available online 1999)
卷期:
Volume 27,
issue 6
页码: 2701-2732
ISSN:0092-7872
年代: 1999
DOI:10.1080/00927879908826588
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
Unital quadratic Jordan algebrasJ(q, I) determined by nondegenerate quadratic forms with basepoints over a field axe called full Jordan Clifford algebras. In characteristic 2 they have ample outer ideals which are also simple; they come in 3 sizes, tiny, small, and large, where the large are full Clifford algebras but the tiny and small algebras are lacking some of their parts. The simple algebras played a role in Zelmanov's solution of the Burnside Problem. In this paper we will analyze these in more detail, determining their centroids and their local algebras; this is important in the classification of prime Jordan triples of Clifford type in arbitrary char-acterstics. In addition we make a careful charcterization of the tiny, small, and large Clifford algebras. We use this to straighten one or two missteps in a proof from the classification of simple algebras. An important role in our characterization is played by commutators, and we describe the Jordan commutator products and Bergmann formulas for Clifford algebras in general.
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