The Role of Nonassociative Algebra in Projective Geometry (Graduate Studies in Mathematics, 159, Band 159) - Hardcover

Faulkner, John R.

9781470418496: The Role of Nonassociative Algebra in Projective Geometry (Graduate Studies in Mathematics, 159, Band 159)

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ISBN 10: 1470418495 ISBN 13: 9781470418496

Verlag: American Mathematical Society, 2014

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Faulkner provides graduate mathematics students a largely self-contained, in-depth account of linkages between the two branches of mathematics, presenting several new results and mostly new proofs. Students are assumed to know linear algebra, basic ring theory, and basic group theory and to be able to follow a detailed proof. Among the topics are central automorphisms of projective planes, configuration conditions, quadratic forms and orthogonal groups, norms and hermitian matrices, and projective remoteness planes. Annotation �2014 Ringgold, Inc., Portland, OR (protoview.com)

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John R. Faulkner, University of Virginia, Charlottesville, VA, USA.

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Verlag: American Mathematical Society
Erscheinungsdatum: 2014
Sprache: Englisch
ISBN 10: 1470418495
ISBN 13: 9781470418496
Einband: Gebundene Ausgabe
Anzahl der Seiten: 229
Kontakt zum Hersteller: Nicht verf�gbar
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The Role of Nonassociative Algebra in Projective Geometry (Graduate Studies in Mathematics)

Faulkner, John R.

Verlag: American Mathematical Society, 2015

ISBN 10: 1470418495 ISBN 13: 9781470418496

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Zustand: New. 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. . 2015. hardcover. . . . . Bestandsnummer des Verk�ufers V9781470418496

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The Role of Nonassociative Algebra in Projective Geometry

Faulkner, John R.

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ISBN 10: 1470418495 ISBN 13: 9781470418496

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Hardcover. Zustand: Brand New. 233 pages. 10.25x7.50x0.75 inches. In Stock. Bestandsnummer des Verk�ufers __1470418495

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Role of Nonassociative Algebra in Projective Geometry

Faulkner, John R.

Verlag: American Mathematical Society, 2014

ISBN 10: 1470418495 ISBN 13: 9781470418496

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The Role of Nonassociative Algebra in Projective Geometry

John R. Faulkner

Verlag: American Mathematical Society, US, 2014

ISBN 10: 1470418495 ISBN 13: 9781470418496

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Hardback. Zustand: New. 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. Bestandsnummer des Verk�ufers LU-9781470418496

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