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The Role Of Nonassociative Algebra In Pr
John R. Faulkner
€ 146.45
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Description for The Role Of Nonassociative Algebra In Pr
Hardback. Series: Graduate Studies in Mathematics. Num Pages: 233 pages. BIC Classification: PBF; PBMW; PBP. Category: (P) Professional & Vocational. Dimension: 262 x 190 x 15. Weight in Grams: 594.
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.
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.
Product Details
Format
Hardback
Publication date
2014
Publisher
American Mathematical Society United States
Number of pages
233
Condition
New
Series
Graduate Studies in Mathematics
Number of Pages
233
Place of Publication
Providence, United States
ISBN
9781470418496
SKU
V9781470418496
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About John R. Faulkner
John R. Faulkner, University of Virginia, Charlottesville, VA, USA.
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