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Points and Lines: Characterizing the Classical Geometries
Ernest E. Shult
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Description for Points and Lines: Characterizing the Classical Geometries
Paperback. All the geometries covered in this book, including those arising from Lie-type groups, are characterized by easily understood local axioms on points and lines. The self-contained presentation proceeds step-by-step from elementary first principles. Series: Universitext. Num Pages: 698 pages, 88 black & white illustrations, biography. BIC Classification: PBM. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 33. Weight in Grams: 1002.
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to ... Read more
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to ... Read more
Product Details
Format
Paperback
Publication date
2010
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Number of pages
698
Condition
New
Series
Universitext
Number of Pages
676
Place of Publication
Berlin, Germany
ISBN
9783642156267
SKU
V9783642156267
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
About Ernest E. Shult
Ernest Shult studied finite groups with Michio Suzuki, and held visiting fellowships at the University of Chicago and the Princeton Institute for Advanced Study in the 1960’s. He continued to contribute to finite groups until he got interested in incidence geometry. In 1987-8, he received a US Scientist Award from the Alexander von Humboldt Foundation in Freiburg Germany.
Reviews for Points and Lines: Characterizing the Classical Geometries
From the reviews: “In this expansive volume, Shult (Kansas State Univ.) attempts to provide a thorough, self-contained characterization of geometries of Lie type by means of local axioms on points and lines. … There is enough material here for several semester-long graduate courses; alternatively, the book could be used as a reference work. Shult makes every effort to remain ... Read more