000			05157nam a22004693i 4500
001			EBC3330427
003			MiAaPQ
005			20240729125050.0
006			m o d |
007			cr cnu||||||||
008			240724s2009 xx o ||||0 eng d
020			_a9781614446040 _q(electronic bk.)
020			_z9780883857595
035			_a(MiAaPQ)EBC3330427
035			_a(Au-PeEL)EBL3330427
035			_a(CaPaEBR)ebr10733070
035			_a(OCoLC)929120365
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA387.P65 2009eb
082	0		_a512.482
100	1		_aPollatsek, Harriet.
245	1	0	_aLie Groups : _bA Problem Oriented Introduction Via Matrix Groups.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2009.
264		4	_c©2009.
300			_a1 online resource (190 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_acover -- copyright page -- title page -- Preface -- Notational Conventions -- Contents -- 1 Symmetries of vector spaces -- 1.1 What is a symmetry? -- 1.2 Distance is fundamental -- 1.3 Groups of symmetries -- 1.4 Bilinear forms and symmetries of spacetime -- 1.5 Putting the pieces together -- 1.6 A broader view: Lie groups -- 2 Complex numbers, quaternions and geometry -- 2.1 Complex numbers -- 2.2 Quaternions -- 2.3 The geometry of rotations of R^3 -- 2.4 Putting the pieces together -- 2.5 A broader view: octonions -- 3 Linearization -- 3.1 Tangent spaces -- 3.2 Group homomorphisms -- 3.3 Differentials -- 3.4 Putting the pieces together -- 3.5 A broader view: Hilbert's fifth problem -- 4 One-parameter subgroups and the exponential map -- 4.1 One-parameter subgroups -- 4.2 The exponential map in dimension 1 -- 4.3 Calculating the matrix exponential -- 4.4 Properties of the matrix exponential -- 4.5 Using exp to determine L.G/ -- 4.6 Differential equations -- 4.8 A broader view: Lie and differential equations -- 4.9 Appendix on convergence -- 5 Lie algebras -- 5.1 Lie algebras -- 5.2 Adjoint maps-big 'A' and small 'a' -- 5.3 Putting the pieces together -- 5.4 A broader view: Lie theory -- 6 Matrix groups over other fields -- 6.1 What is a field? -- 6.2 The unitary group -- 6.3 Matrix groups over finite fields -- 6.4 Putting the pieces together -- Suggestions for further reading -- 6.5 A broader view: finite groups of Lie type and simple groups -- Appendix I Linear algebra facts -- Appendix II Paper assignment used at Mount Holyoke College -- Appendix III Opportunities for further study -- Metric vector spaces and symmetries -- Lie algebras and Chevalley groups -- Quaternions and octonions -- Connections to physics -- Lie groups as manifolds -- Solutions to selected problems -- 1. Symmetries of vector spaces -- 1.1. What is a symmetry?.
505	8		_a1.2. Distance is fundamental -- 1.3. Groups of symmetries -- 1.4. Bilinear forms and symmetries of spacetime -- 2. Complex numbers, quaternions and geometry -- 2.1. Complex numbers -- 2.2. Quaternions -- 2.3. The geometry of rotations of R^3 -- 3. Linearization -- 3.1. Tangent spaces -- 3.2. Group homomorphisms -- 3.3. Differentials -- 4. One-parameter subgroups and the exponential map -- 4.1. One-parameter subgroups -- 4.2. The exponential map in dimension 1 -- 4.3. Calculating the matrix exponential -- 4.4. Properties of the matrix exponential -- 4.5. Using exp to determine L.G/ -- 4.6. Differential equations -- 5. Lie algebras -- 5.1. Lie algebras -- 5.2. Adjoint maps-big 'A' and small 'a' -- 6. Matrix groups over other fields -- 6.1. What is a field? -- 6.2. The unitary group -- 6.3. Matrix groups over finite fields -- Bibliography -- Index -- Notation -- About the Author.
520			_aThis textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called "Putting the pieces together" in which all definitions and results are collected for reference and further reading is suggested.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aLie groups.
650		0	_aLie groups -- Problems, exercises, etc.
650		0	_aMatrix groups.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aPollatsek, Harriet _tLie Groups _dProvidence : American Mathematical Society,c2009 _z9780883857595
797	2		_aProQuest (Firm)
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3330427 _zClick to View
999			_c79880 _d79880