This is the list of misprints and errors that have been found so far in the book

Symmetries, Lie algebras and representations

( Cambridge University Press )  by  Jürgen Fuchs  and  Christoph Schweigert  .

If you think you have discovered another typo or if you have any other
remark on the book, feel free to send mail to the authors.

List of Errata:

 

p. 15

eq. (1.36)

In order to have the same convention as in eq. (1.15), the right hand side should be multiplied by  –1 .

detected by   Jose Ignacio   Rosado

 

p. 24

after eq.   (2.28)

The term  "right hand side"  must be replaced by  "left hand side" .

detected by   Jose Ignacio   Rosado

 

p. 32

eqs. (3.6)   & (3.7)

The sign of the second term on the right hand side of the first line must be  +  rather than  – .

detected by   Jose Ignacio   Rosado

 

p. 34

5th line   after eq.   (3.13)

The equation number  "(3.12)" must be replaced by  "(3.11)" .

detected by   Ingo   Runkel

 

p. 36

eqs.  (3.18)   & (3.19)

The Lie algebra generator, respectively matrix,  σ2 is defined as  minus  the expression given in the book.

detected by   Stefan   Dittmaier

 

p. 40

eq. (3.33)

The number  "√3"  in front of HY  must be replaced by its inverse, i.e. by   "1/√3".

detected by   Patrik   Svantesson

 

p. 40

3rd & 2nd lines before eq.    (3.35)

The terms  "creation operators"  and  "annihilation operators" must be interchanged.

detected by   Jose Ignacio   Rosado

 

p. 44

picture     (3.42)

The root system in the left figure is the one of  C2  rather than the one of the (isomorphic) Lie algebra  B2. To get the root system of B2 one must interchange the simple roots  α(1) and  α(2).

detected by   Antonin   Pottier

 

p. 50

bottom

In the definition of a hermitian product  μ  one must in addition include the property that   μ(v,w) = μ(w,v)* .

detected by   Helmuth   Urbantke

 

p. 57

last sentence

The statement is incorrect. Lie algebras with   [g,g]  =  g   are called perfect ; this property is strictly weaker than semisimple. A standard example of a non-semisimple perfect Lie algebra is the Poincare algebra.

detected by   Per   Salomonson

 

p. 58

4th line   after eq.   (4.33)

The formulation  "contains E + (E–)"  must be replaced by "contains E– (E+ )" .

detected by   Eric-Olivier   Le Bigot

 

p. 58

4th line   after eq.   (4.33)

The term  "subalgebra"   must be replaced by  "ideal" .

 

p. 64

around   eq. (5.2)

The terms  "space V"  in the second line before eq. (5.1) and  "set V"  in the fourth line after eq. (5.2) must be replaced by  "vector space V" .

detected by   Helmuth   Urbantke

 

p. 69

eq. (5.17)

The  +  sign on the right hand side must be replaced by an  ⊕  symbol.

detected by   Albrecht   Wurtz

 

p. 74

5th line   after eq.   (5.24)

The text  "all finite-dimensional modules" must be replaced by  "all irreducible finite-dimensional modules" .

detected by   Ingo   Runkel

 

p. 76

eq. (5.32)

In the formulas for the case of Bn the following changes should be made: First, in the set B+ the expression  " Ei,j+n+Ej,i+n"  must be replaced by  " Ei,j+n–Ej,i+n". Second, both for B+ and B– the case  i = j  (for which the matrix is just zero) must be omitted.

detected by   Henric   Larsson

 

p. 79

Summary

In the second sentence, the term  "Any Lie algebra" must be replaced by  "Any semisimple Lie algebra" .

detected by   Eric-Olivier   Le Bigot

 

p. 88

paragraph   after (6.18)

All occurrences of the summation range  N  (natural numbers)  must be replaced by  Z  (all integers).

detected by   Werner   Wetzel

 

p. 89

1st line after   eq. (6.20)

The term  " semisimple "  must be replaced by  " simple ".

detected by   Albrecht   Wurtz

 

p. 91

last 2 lines

The statement that the simple roots are those positive roots closest to the hyperplane that separates positive from negative roots is wrong.

detected by   Thomas   Fischbacher

 

p. 102

eq. (6.75)

In the fourth equation in the right, all the symbols  " Eθ "  must be replaced by  " E±θ ".

detected by   Teake   Nutma

 

p. 103

line 18

At the end of the line, the term  " simple "  must be replaced by  " semisimple ".

detected by   Antonin   Pottier

 

p. 117

table VI

The first three entries in the last row of the quadratic form matrix for Ar   are   1 2 3   rather than   1 2 2 . The second entry in the third row is   2 (r – 2)   rather than   2 (r – 1) .

 

p. 123

line 10

The phrase  " if an only if "  should read  " if and only if ".

 

p. 135

after eq.   (8.9)

The restriction that the Killing form should be of the special form (8.8) is unnecessary.

 

p. 143

Exercise   (8.3)

The restriction that the Killing form should be of the special form (8.8) is unnecessary. The second part of the hint is therefore irrelevant, too.

 

p. 143

eq. (8.20)

The range of \alpha does not consist of all roots, but only of the  positive roots .

 

p. 163

eq. (10.7)

The equation should read   Mwt G Mw = G ,   with  G  the quadratic form matrix.

detected by   Paul   Skerritt

 

p. 168

3rd line   after eq.   (10.22)

The Weyl group of  An = su(n+1)  has  (n+1)!  rather than  n!  elements.

detected by   Johannes   Walcher

 

p. 169

eq.  (10.26)

The formula for the simple root α(2) reads  α(2) = (0,1,–1,0,...,0)  rather than  (1,0,–1,0,...,0) .

 

p. 222

line 6

Replace  "R(λ)" by  "V(λ)" .

detected by   Jakob    Palmkvist

 

p. 249

13th line   from bottom

On the right hand side of the second equation, the vector  vΛ  should be replaced by the vector   x vΛ .

detected by   Christian    Stahn

 

p. 303

eq. (17.5)   - (17.7)

Each occurrence of the subscript  "jm" must be replaced by  "jn" . (Once in eq. (17.5), twice in eq. (17.6), once in the 1st line after (17.6), once in the 2nd line after (17.6), twice in eq. (17.7).)

detected by   Jakob    Palmkvist

 

p. 305

eq. (17.13)

In the formulas in the third and fourth line, the right hand side must be multiplied by  –1 .

detected by   Björn    Haßler

 

p. 342

line 19

The expression  "x ⊗ y" must be replaced by "x ⊗ y + y ⊗ x" .

detected by   Ingo    Runkel

 

p. 361

Ex. 20.6

Replace the formulation  "Identify ... with"  by  "Relate ... to"

 

p. 375

eq. (21.39)

The left bracket   "("   in front of   "cos"   must be removed.

 

p. 377

after eq.   (21.44)

The word   "with"   in the first line after eq. (21.44) must be removed.

 

p. 377

before eq.   (21.45)

In the parametrization of SU(2) elements a factor of   i   (imaginary unit) is missing in the second term. Thus the correct expression reads   ξ01  + i ∑i=1,2,3 ξi σi .

 

p. 379

after eq.   (21.51)

In order to generate the algebra of continuous functions on the group manifold of  G = SU(n)  (which is a dense subalgebra of the algebra  L2(G)  of square integrable functions), it is sufficient to take the matrix elements of the fundamental representation with highest weight  \Lambda(i)                 for an arbitrary  single i , rather than - as erroneously stated in the book - the matrix elements of  all  fundamental representations. For more information, we refer to the relevant addendum.

detected by   Andrew    Jacobs

 

p. 391

eq.   (22.28)

The first of the four relations must read   " ε(e) = 1 "   rather than   " ε(e) = e ". (Here  e  is the unit element in the universal enveloping algebra, while   1  is the unit in the base field.)

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Last modified:     Fri Mar 9 16:36:32 CET 2007