Universitext

By: Morton Landers Curtis, M. L. Curtis

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Paperback | 31 October 1984 | Edition Number 2

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228 Pages

Edition Type
Revised

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23.5 x 15.88 x 1.27

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These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphic. In Chapter I "group" is defined and examples are given; ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A ~ 0 , and define the general linear group GL(n,k) We construct the skew-field lli of to operate linearly on llin quaternions and note that for A E Mn(lli) we must operate on the right (since we mUltiply a vector by a scalar n on the left). So we use row vectors for R , en, llin and write xA for the row vector obtained by matrix multiplication. We get a ~omplex-valued determinant function on Mn (11) such that det A ~ 0 guarantees that A has an inverse.

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Algebra

General Linear Groups
Orthogonal Groups
Homomorphisms
Exponential and Logarithm
SO(3) and Sp(1)
Topology
Maximal Tori
Covering by Maximal Tori
Conjugacy of Maximal Tori
Spin(k)
Normalizers, Weyl Groups
Lie Groups
Reflections, Roots
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Universitext

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