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Titlebook: Generators and Relations in Groups and Geometries; A. Barlotti,E. W. Ellers,K. Strambach Book 1991 Kluwer Academic Publishers 1991 Algebra

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书目名称Generators and Relations in Groups and Geometries
编辑A. Barlotti,E. W. Ellers,K. Strambach
视频videohttp://file.papertrans.cn/383/382374/382374.mp4
丛书名称Nato Science Series C:
图书封面Titlebook: Generators and Relations in Groups and Geometries;  A. Barlotti,E. W. Ellers,K. Strambach Book 1991 Kluwer Academic Publishers 1991 Algebra
描述Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann‘s work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char­ acterization are natural and plausible. They provoke the stu
出版日期Book 1991
关键词Algebraic structure; algebra; algebraic group; automorphism; differential geometry; matrix theory
版次1
doihttps://doi.org/10.1007/978-94-011-3382-1
isbn_softcover978-94-010-5496-6
isbn_ebook978-94-011-3382-1Series ISSN 1389-2185
issn_series 1389-2185
copyrightKluwer Academic Publishers 1991
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Book 1991oded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char­ acterization are natural and plausible. They provoke the stu
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Classical Groupshe structure of the group. It is advantageous to determine the minimal number of factors needed to express an element as a product of generators. This number is called the length of a group element. The Cartan-Dieudonné theorem is a well-known example for results of this kind..The classical groups h
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Generators of Automorphism Groups of Cayley Algebrasms needed to express an automorphism of . is called its length. For Cayley algebras . over fields of characteristic not 2 we determine the length of any automorphism of .. It turns out that every automorphism of a Cayley algebra is the product of at most three involutory automorphisms. Hence the aut
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Products of Matricesof .(.). In particular, we consider the following types of decomposition:.While most of the discussion concerns matrices over a field, we refer briefly to the case where the matrices in question have integer entries.
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