Matrix Groups: An Introduction to Lie Group Theory by Andrew Baker

Published November 2001; reprinted August 2003

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Corrections and comments

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Corrections to the second printing

Page 68, line 3: the Jacobi identity should be


Page 106, Prop. 4.21: u statement should end with `...and each Ae_i is a simple algebra.'.

Page 140, line 1: u should be an element of Gamma_n.

Corrections to the first printing

Page vii, Some suggestions for reading this book

Line 4: `Chapters 1,3,7' should be `Chapters 1,2,3,7'.

Page 6, line 8

Second `M_n(R)' should be `M_n(C)'.

Page 12, section 1.3, line 4:

`domain' should be `codomain'.

Page 15, proof of 1.29, line 3:

the first term should be `$rho(x,s_n)'.

Page 17, line 17:

The end of the equation should be `...=det^{-1}R^+'.

Page 47, line -4:

The end of the sequence of equations should be `...=exp(A+B)'.

Page 50, Proof of Proposition 2.5

This result would probably have been better put later in the chapter after the material on one-parameter subgroups. Here is a rewritten version (07/05/2002) with some more details about what goes into the proof which follows that outlined by G. Segal in [4], page 80.

Page 54, Theorem 2.9, line -2:

The expression at the end of the line should be `J(lambda_j,r_j)'.

Page 58, line -1:

The equation should be `gamma'(t)=gamma(t)A'.


Page 60-1, Example 2.20

The intended value of v(0) was [0 0 1]^T, and in the Solution the (2,2) term of the matrix exp(tS) needs an extra factor of 5. Here is a rewritten version (14/05/2002).

Page 63, line 4:

The last equation should read `...=ce^{2t}'.

Page 71, line 8:

The second `={0}' should be deleted.

Page 75, line -12:

Equation should read `...with alpha(0)=I'.

Page 83 line 18:

It should read `dim Sk-Herm_n(C)=n+2....'.

Page 88, line -2:

`ker Ad' should be just `Ad'.

Page 89, line 19:

It should be `U_2 = x_2 H^ + y_2 E^ + z_2 F^'.

Page 91, line -5:

Final `H^' should be `H'.

Page 91, line 8:

`cos' should be `cos phi'.

Page 103, line 4:

The left hand side of the equation should be `av_j'.

Page 103, Proof of lemma 4.12:

This should read `If a in ker lambda then a1=0, so a=0.'

Page 103, line -1:

This should read `(-1,-1) in ker lambda^times times rho^times, -1 in ker Delta.

Page 108, Example 4.25:

In the expression for $e_3$, 1/6 should be 1/3.

Page 111, line 14 after Defn 4.31:

`nu(a,b)<=nu(a)nu(b)' should be `nu(a,b)=nu(a)nu(b)''.

Page 114, Prop 4.37, 2nd equation:

The sum on the left side should be from 1 to m, not 1 to n, and the sum of the right side should be over r not s. In the next equation, the x's should go from 1 to m.

Page 119, line 6:

`... k = i = -kj ...' should be `... jk = i = -kj ...'.

Page 120, line 14:

`z=' should be `z=u1 + vi'.

Page 125, Example 4.52, line 7:

The middle equation should read `alpha(j)=Aj'.

Page 128, Question 4.9, line 2:

The equation should read `...=dim Symp_{2n}(R)'.

Page 130, equation (5.1)

`e_se_r = -e_se_r' should be `e_se_r = -e_re_s'.

Page 134, line -7:

The second `=' is missing.

Page 163, Proposition 6.6

`U_k=...' should be `U_j=...'.

In the equation for <U_j,U_k>, the last case should read `if j=k=n+1'.

Page 165, line -7:

The 2 times 2 matrix should be R(theta) (with no subscript).

Page 169, line -3:

In the definition of U'', the factor in front should be `1/2i'.

Page 171, Section 6.3, line 1:

Should read `the Lie algebra of'.

Page 182, Definition 7.2:

This should read `A topological space X is separable if it has a countable basis, i.e., a basis of the form...'.

Page 182, Definition 7.3, line 4:

Should read `...a collection of n-charts'.

line -10:

The domain of `f_0 circ gamma' should be`(a,b) cap gamma^{-1}f_0^{-1}V_0'.

line -7:

The domain of `f_0 circ gamma' should be `(a,b) cap gamma^{-1}f^{-1}V_0'.

Page 184, line 7:

`(f\gamma)'(0)' should be `(f_0\gamma)'(0)'.

Page 193, lines -9, -7, -5:

In each case, the sums should be over `k=>2' rather than `k<=2'.

Page194, line 14

1/2||C||^2 should be 1/2||C||.

Page 205, line -3, -1:

In each case the second vector should be `(0,1,0)'.

Page 206, line -9:

Should read `...which shows that phi(g) v is another'.

Page 206, line -2:

Should read `...there are non-zero vectors'.

Page 212, line -14:

`pi U subset G' should be `pi U subset G/H'.

Page 213, diagram:

The right hand arrow should be labelled with `f' and the bottom arrow with `overline{f}'.

Page 242, line 7:

`p(0)=x and q(0)=y' should be `p(1)=x and q(1)=y'.

Page 308, line -1:

The (2,1) entry `-2n' in the matrix on the right hand side should be `-2nt^{n-1}'.

Principal vs Principle

Yes I know, Principle in Theorems 10.13 & 10.15 (and anywhere else) should be Principal.


Thanks to R. Barraclough, R. Chapman, P. Eccles, Robin Endelman, S. Hendren, N. Pollock, M. Yankelevitch and R. Wickner for spotting the above.

Andrew Baker (email)

Last updated on   6th November 2007 Page maintained by   Andrew Baker