000			03483nam a22004455i 4500
001			u375087
003			SIRSI
005			20160812084306.0
007			cr nn 008mamaa
008			101211s2011 gw | s |||| 0|eng d
020			_a9783642156274 _9978-3-642-15627-4
040			_cMX-MeUAM
050		4	_aQA440-699
082	0	4	_a516 _223
100	1		_aShult, Ernest. _eauthor.
245	1	0	_aPoints and Lines _h[recurso electrónico] : _bCharacterizing the Classical Geometries / _cby Ernest Shult.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011.
300			_aXXII, 676p. 88 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext
505	0		_aI.Basics -- 1 Basics about Graphs -- 2 .Geometries: Basic Concepts -- 3 .Point-line Geometries.-4.Hyperplanes, Embeddings and Teirlinck's Eheory -- II.The Classical Geometries -- 5 .Projective Planes.-6.Projective Spaces -- 7.Polar Spaces -- 8.Near Polygons -- III.Methodology -- 9.Chamber Systems and Buildings -- 10.2-Covers of Chamber Systems -- 11.Locally Truncated Diagram Geometries.-12.Separated Systems of Singular Spaces -- 13 Cooperstein's Theory of Symplecta and Parapolar Spaces -- IV.Applications to Other Lie Incidence Geometries -- 15.Characterizing the Classical Strong Parapolar Spaces: The Cohen-Cooperstein Theory Revisited -- 16.Characterizing Strong Parapolar Spaces by the Relation between Points and Certain Maximal Singular Subspaces -- 17.Point-line Characterizations of the “Long Root Geometries” -- 18.The Peculiar Pentagon Property.
520			_aThe 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 recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.
650		0	_aMathematics.
650		0	_aTopological Groups.
650		0	_aGeometry.
650	1	4	_aMathematics.
650	2	4	_aGeometry.
650	2	4	_aTopological Groups, Lie Groups.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642156267
830		0	_aUniversitext
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-15627-4
596			_a19
942			_cLIBRO_ELEC
999			_c202967 _d202967