Representations and Cohomology: Errata etc.
D. J. Benson
Mathematical Institute
24-29 St. Giles
Oxford OX1 3LB
Great Britain
March 31, 1993
1 Volume I
p. (x) l. 5, "Chapter 4" should read "Chapter 6".
p. 24-25: As it stands, the proof of Lemma 2.2.3 is wrong, because is not *
*necessarily
surjective. However, if P is a finitelygenerated projective module, then the pr*
*oof works. So
at the beginning of the section,one should make the further observation that P=*
* F0( )
is a finitely generated projective module. This is because among all pro jectiv*
*e modules,
one can recognise the finitely generatedones as those for which
1M M1
Hom (P; P )= Hom (P;P ):
i=1 i=1
To see this, one looks at thisequation with in place of the left-hand variabl*
*e, and
looks at where the identity element goes. So we demand that a progenerator be a*
* finitely
generated projective module in Definition 2.2.1.
This also means that Exercises 1-3 of this section need changing. In Exercis*
*e 3, take
away the multiples ofthe identity, so that Mat1 () is a ring without identity.
Delete the remark on p. 24, which is misleading.
p. 26 l. 17, "Chapter 7" should read "Chapter 1 of Volume II".
p. 28 l. -3, "amd" should read "and".
p. 29 l. -6, "Ker (@n)" should read "Ker (@n1 )".
p. 35 l. -8, "sequence" should read "sequences".
p. 39 l. 10 delete "of -modules".
p. 40 l. 15, "Section 9.6" should read "Section 3.6of Volume II".
p. 40 l. -6, "f(@n1 (x))" should read "f(@n+1 (x))".