Author | Curtis, Morton L. author |
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Title | Matrix Groups [electronic resource] / by Morton L. Curtis |
Imprint | New York, NY : Springer US, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0093-9 |
Descript | XII, 191 p. online resource |
1 General Linear Groups -- A. Groups -- B. Fields, Quaternions -- C. Vectors and Matrices -- D. General Linear Groups -- E. Exercises -- 2 Orthogonal Groups -- A. Inner Products -- B. Orthogonal Groups -- C. The Isomorphism Question -- D. Reflections in Rn -- E. Exercises -- 3 Homomorphisms -- A. Curves in a Vector Space -- B. Smooth Homomorphisms -- C. Exercises -- 4 Exponential and Logarithm -- A. Exponential of a Matrix -- B. Logarithm -- C. One-parameter Subgroups -- D. Lie Algebras -- E. Exercises -- 5 SO(3) and Sp(1) -- A. The Homomorphism ? : S3 ? SO(3) -- B. Centers -- C. Quotient Groups -- D. Exercises -- 6 Topology -- A. Introduction -- B. Continuity of Functions, Open Sets, Closed Sets -- C. Connected Sets, Compact Sets -- D. Subspace Topology, Countable Bases -- E. Manifolds -- F. Exercises -- 7 Maximal Tori -- A. Cartesian Products of Groups -- B. Maximal Tori in Groups -- C. Centers Again -- D. Exercises -- 8 Covering by Maximal Tori -- A. General Remarks -- B. (โ ) for U(n) and SU(n) -- C. (โ ) for SO(n) -- D. (โ ) for Sp(n) -- E. Reflections in Rn (again) -- F. Exercises -- 9 Conjugacy of Maximal Tori -- A. Monogenic Groups -- B. Conjugacy of Maximal Tori -- C. The Isomorphism Question Again -- D. Simple Groups, Simply-Connected Groups -- E. Exercises -- 10 Spin(k) -- A. Clifford Algebras -- B. Pin(k) and Spin(k) -- C. The Isomorphisms -- D. Exercises -- 11 Normalizers, Weyl Groups -- A. Normalizers -- B. Weyl Groups -- C. Spin(2n+1) and Sp(n) -- D. SO(n) Splits -- E. Exercises -- 12 Lie Groups -- A. Differentiable Manifolds -- B. Tangent Vectors, Vector Fields -- C. Lie Groups -- D. Connected Groups -- E. Abelian Groups