On algebras of rank three
作者:
Sebastian Walcher,
期刊:
Communications in Algebra
(Taylor Available online 1999)
卷期:
Volume 27,
issue 7
页码: 3401-3438
ISSN:0092-7872
年代: 1999
DOI:10.1080/00927879908826635
出版商: Gordon and Breach Science Publishers Ltd.
关键词: 17A01;17A30;17A75;17B25;16G99
数据来源: Taylor
摘要:
An algebra of rank three is a commutative, finite dimensional algebra that may be defined by the property that every element generates a subalgebra of dimension not greater than two. In this article we discuss several classes of such algebras, including two classes related to central simple Jordan algebras, and derive some general results which indicate that, with the exception of one pathological class related to nilpotent algebras, every rank three algebra can be constructed either from a quadratic and alternative algebra or from a representation of a Clifford algebra. Among other results, semisimple and simple rank three algebras are characterized, and the radical of an arbitrary rank three algebra is determined.
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