
Introduction  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2014; 229 pp; hardcover Volume: 159 ISBN10: 1470418495 ISBN13: 9781470418496 List Price: US$67 Member Price: US$53.60 Order Code: GSM/159 See also: Graduate Algebra: Noncommutative View  Louis Halle Rowen Parabolic Geometries I: Background and General Theory  Andreas Cap and Jan Slovak  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 selfcontained, indepth 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 and relates coordinate properties to transitivity properties of certain automorphisms and to configuration conditions. It also classifies higherdimensional 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. Readership Graduate students and research mathematicians interested in nonassociative algebra and projective geometry; physicists interested in division algebras and string theory. 


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