Blocks of Finite Groups The Hyperfocal Subalgebra of a Block
About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-bl
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Springer-Verlag Berlin Heidelberg GmbH
Lluls Puig ~Jb$Jj- • -!V $
;ff Ftt jf Blocks of
~ #c Finite Groups
#t at.; ~ 1R. ~, -r1\4t
The Hyperfocal Sub algebra of a Block
Springer
Lluis Puig Universite de Paris 7 - Denis Diderot Institut de Mathematiques de Jussieu 175, rue du Chevaleret 75013 Paris, France e-mail: [email protected]
Catalog-in-Publication Data applied for Die Deutsche Bibliotbek - CIP-Einheitsaufnahme Puig, Uufs: Blocks of finite groups: tbe hyperfocal subalgebra of a block /UuisPuig. (Springer monographs in matbematics) ISBN 978-3-662-11256-4 (eBook) ISBN 978-3-642-07802-6 DOI 10.1007/978-3-662-11256-4
Mathematics Subject Classification (2000): 20Cn
ISBN 978-3-642-07802-6
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Contents i .................... 1
1. Introduction .......................... 1
2. iJ-~7Gl¥Jf;t1t- .......... 7
2. Lifting Idempotents ................... 7
3.0-1\4fH'-1.S;, *'Al¥J1t4ft ............ 19
3. Points of the O-algebras and Multiplicity of the Points ........ 19
4. N-F9 G-1\4ftJ:.a'-1ft-t .. 31
4. Divisors on N-interior G-algebras .... 31
5. ft-ta'-1 ftl1jil] :f"ft-tl¥Jjj}~ ......... 41
5. Restriction and Induction of Divisors ........................... 41
6. N-F9 G-1\4ftJ:. l¥J A'J-%F A~f ............ 53
6. Local Pointed Groups on N-interior G-algebras ............. 53
7. 10 Green
7. On Green's Indecomposability Theorem .......... 65
1. iJ)
::f!if 7J'- fij'H1. Jt J.'f. . . . . . . 65 8. ~~#N-F9G-1\4ftJl. .. 71 9. G-F91\4ft
Ej N -F9 G-1\ 4ft iJ'J ~
.... 85 10. Xif 1\ 4ftJ:. a'-1 .s;,Xif ........ .
8. Fusions in N-interior G-algebras ..... 71 9. N-interior G-algebras through G-interior AIgebras .......... 85
....................... 99
10. Pointed Groups on the Group Algebra ................ 99
11. G-Jjcl¥J~~Z-1\4ft ... 121
11. Fusion Z-algebra of a Block ......... 121
12. G-Jjca'-1~1\4ft. .
