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This is a list of misprints and errors that have been found in the book
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SYMMETRIES, LIE ALGEBRAS AND REPRESENTATIONS
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( Cambridge University
Press ) by
Jürgen Fuchs and
Christoph Schweigert
.
We are grateful to many colleagues for their feedback.
If you think you have discovered another typo or
if you have any other remark on the book, we appreciate your feedback.
( For our email addresses see our home pages:
JF /
CS )
| page 15 | eq. (1.36) | In order to have the same convention as in eq. (1.15),
the right hand side must be multiplied by –1 . | detected by
Jose Ignacio
Rosado |
| page 24 | after
eq. (2.28) | The term "right hand side" must be replaced by "left hand side" . | detected by
Jose Ignacio
Rosado |
| page 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 |
| page 34 | 5th line after
eq. (3.13) | The equation number " (3.12) " must be replaced by " (3.11) " . | detected by
Ingo
Runkel |
| page 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 |
| page 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 |
| page 40 | 3rd & 2nd
lines before
eq. (3.35) | The terms "creation operators" and "annihilation operators" must be interchanged. | detected by
Jose Ignacio
Rosado |
| page 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 thesimple roots α(1) and α(2). | detected by
Antonin
Pottier |
| page 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 |
| page 51 | Section 4.4 | The symbol "GL( n,F)" must be replaced by "Mat( n×n,F)" .
The phrase "and SL( n,F) of n×n matrices of unit determinant "
must be deleted altogether. | detected by
Michael
Baker |
| page 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 Poincaré algebra. | detected by
Per
Salomonson |
| page 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 |
| page 58 | 4th line after
eq. (4.33) | The term "subalgebra" must be replaced by "ideal" . | |
| page 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 |
| page 68 | eq. (5.14) | The expression on the right hand side must be multiplied by a minus sign, i.e. the correct expression is −fabc . | detected by
Howard
Haber |
| page 69 | eq. (5.17) | The + sign on the right hand side must be replaced by a ⊕ symbol. | detected by
Albrecht
Wurtz |
| page 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 |
| page 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 |
| page 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 |
| page 80 | Exercise 5.4 | Delete the first part of the exercise; the assertion in this part is wrong.
(The statement in the application to the adjoint representation is, however, correct.) | detected by
Timm von
Puttkammer |
| page 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 |
| page 88 | 2nd paragraph
before
eq. (6.18) | In the definition of the subspace k ,
g0 must be replaced by spanC(Hα) | detected by
Philippe
Spindel |
| page 89 | 1st line after
eq. (6.20) | The term " semisimple " must be replaced by " simple ". | detected by
Albrecht
Wurtz |
| page 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 |
| page 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 |
| page 102 | last line of
eq. (6.75) | The right hand side of the last equation must be multiplied by −1
Thus the prefactor of the step operator on the right hand side is ±1 . | detected by
Raphael
Wullschleger |
| page 103 | line 18 | At the end of the line, the term " simple " must be replaced by " semisimple ". | detected by
Antonin
Pottier |
| page 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) . | |
| page 123 | line 10 | The phrase " if an only if " should read " if and only if ". | |
| page 135 | after
eq. (8.9) | The restriction that the Killing form should be of the special form (8.8)
is unnecessary. | |
| page 139 | list of real forms of An-1 | su*(n) is (by definition) equal to sl(n/2,H)
rather than to sl(n/2+1,H) | detected by
Antoine
Van Proeyen |
| page 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. | |
| page 143 | eq. (8.20) | The range of α does not consist of all roots, but of the positive roots only. | |
| page 146 | eq. (9.4) | The signs of the two terms on the right hand side must be interchanged. | detected by
Antoine
Van Proeyen |
| page 150 | 3rd line of
3rd paragraph | The expression w ∈ G must be replaced by w ∈ M . | detected by
Yidun
Wan |
| page 155 | 4th line of
"Information" | Replace " can described " by " can be described " . | detected by
Yidun
Wan |
| page 157 | 3rd line
before
eq. (9,22) | Replace f(0) = 1 by f/0) = 0 . | detected by
Philippe
Spindel |
| page 163 | eq. (10.7) | The equation should read Mwt G Mw = G ,
with G the quadratic form matrix. | detected by
Paul
Skerritt |
| page 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 |
| page 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) . | |
| page 202 | last sentence | The symbol gloop must be replaced by ˜gloop
( i.e. a tilde must be placed over the symbol g ). | detected by
Yidun
Wan |
| page 222 | line 6 | Replace " R(λ) " by " V(λ) " . | detected by
Jakob
Palmkvist |
| page 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 |
| page 253 | line
before
eq. (14,18) | vν must be replaced by vμ . | detected by
Philippe
Spindel |
| page 255 | eq. (14.22) | The expression for the quadratic Casimir on the right hand side must be multiplied by an over-all factor (Iad)-1. | detected by
Howard
Haber |
| page 255 | eq. (14.23) | The expression on the right hand side must be replaced by its inverse, i.e. by 2/(α,α) . | |
| page 255 | eq. (14.24) | In the right-most expression, the prefactor nα must be replaced by its inverse (nα)-1. | |
page 255
/256 | | Analogous replacements as in eq. (14.24),
i.e. nβ by (nβ)-1 , nγ-α by (nγ-α)-1 etc.
must be made in the unnumbered displayed equation above (14.25), in (14.25), in (14.26), and in the unnumbered displayed equation below (14.27). | |
| page 286 | eq. (16.20) | On the left hand side, |J, M⟩ must be replaced by |J, M±1⟩ .
On the right hand side, both occurences of |J, M±1⟩ must be replaced by |J, M⟩ . | detected by
Yidun
Wan |
| page 287 | 2nd line
after
eq. (16.22) | Replace Λ' by Λ1 . | detected by
Igor
Buchberger |
| page 289 | eq. (16.29) | All arrows in the graph on the right hand side must be reversed. | detected by
Igor
Buchberger |
| page 301 | eq. (17.4) | The second occurence of the symbol " R "
must be replaced by " RΛp ". | |
| page 303 | eqs. (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 1stline after (17.6), once in the 2nd line after (17.6), twice in eq. (17.7). ) | detected by
Jakob
Palmkvist |
| page 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 |
| page 342 | line 19 | The expression " x ⊗ y " must be replaced by
" x ⊗ y + y ⊗ x " . | detected by
Ingo
Runkel |
| page 353 | before
eq. (20.38) | Remove the word "antisymmetric" .
( The collection of matrices Mmn satisfies Mmn = −Mnm ,
but the individual matrices need not be antisymmetric. ) | |
| page 361 | Exercise 20.6 | Replace the formulation "Identify ... with" by "Relate ... to" | |
| page 375 | eq. (21.39) | The left bracket " ( " in front of "cos" must be removed. | |
| page 377 | after
eq. (21.44) | The word "with" in the first line after eq. (21.44) must be removed. | |
| page 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 . | |
| page 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 Λ(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 |
| page 387 | 3rd line after
eq. (22.8) | The letter " A " must be typeset in Gothic font. | detected by
Yidun
Wan |
| page 388 | 3rd-to-last line
of 1st paragraph
of 22.2 | The letter " A " must be typeset in Gothic font. | detected by
Yidun
Wan |
| page 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 Jan 10 12:29:12 CET 2014
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