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The Role of Nonassociative Algebra in Projective Geometry

John R. Faulkner (author)

ISBN: 9781470418496

Publication Date: Oct 2014

Format: Hardback

There is a particular fascination when two apparently disjoint areas of mathematics turn out to have a meaningful connection to each other. The main goal of this book is to provide a largely self-contained, in-depth account of the linkage between nonassociative algebra and projective planes, with particular emphasis on octonion planes. There are several new results and many, if not most, of the proofs are new.
£66.50

Temporarily out of stock: usually despatched in 10-14 days

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There is a particular fascination when two apparently disjoint areas of mathematics turn out to have a meaningful connection to each other. The main goal of this book is to provide a largely self-contained, in-depth account of the linkage between nonassociative algebra and projective planes, with particular emphasis on octonion planes. There are several new results and many, if not most, of the proofs are new. The development should be accessible to most graduate students and should give them introductions to two areas which are often referenced but not often taught.

On the geometric side, the book introduces coordinates in projective planes, relates coordinate properties to transitivity properties of certain automorphisms and to configuration conditions. It also classifies higher-dimensional geometries and determines their automorphisms. The exceptional octonion plane is studied in detail in a geometric context that allows nondivision coordinates. An axiomatic version of that context is also provided. Finally, some connections of nonassociative algebra to other geometries, including buildings, are outlined.

On the algebraic side, basic properties of alternative algebras are derived, including the classification of alternative division rings. As tools for the study of the geometries, an axiomatic development of dimension, the basics of quadratic forms, a treatment of homogeneous maps and their polarizations, and a study of norm forms on hermitian matrices over composition algebras are included.
Pages 233
Dimensions 254 x 178
Date Published 30 Oct 2014
Publisher American Mathematical Society
Series Graduate Studies in Mathematics
Series Part 159
Subject/s Algebra   Topology   Geometry   Algebraic geometry  
John R. Faulkner, University of Virginia, Charlottesville, VA, USA.

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