ON THE BLOCK ALGEBRAS HAVING ONLY ONE IRREDUCIBLE MODULE

Authors
ZHANG GX
Citation
Gx. Zhang, ON THE BLOCK ALGEBRAS HAVING ONLY ONE IRREDUCIBLE MODULE, Chinese annals of mathematics. Ser. B, 14(2), 1993, pp. 209-212
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Chinese annals of mathematics. Ser. B → ACNP
ISSN journal
02529599
Volume
14
Issue
2
Year of publication
1993
Pages
209 - 212
Database
ISI
SICI code
0252-9599(1993)14:2<209:OTBAHO>2.0.ZU;2-6
Abstract
The following result is proved: Let B be a block ideal of group algebr a kG over a splitting field k with characteristic p. Suppose that B ha s only one irreducible module L and abelian defect group D, then B con gruent-to Mat(m)(kD), where m = Dim(k) L. This result generalizes Kuls hammer's theorem concerning the structure of block algebras with inert ial index 1.