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The Brauer Group of Irreducible Coalgebras

✍ Scribed by J Cuadra; J.R Garcı́a Rozas; B Torrecillas; F Van Oystaeyen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
159 KB
Volume
238
Category
Article
ISSN
0021-8693

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✦ Synopsis

That is, for a cocommuta-Ž . Ž . Ž . tive irreducible coalgebra C, the homomorphism y *: Br C ª Br C* is injective. The proof uses Morita᎐Takeuchi theory and the linear topology of all closed Ž . cofinite left ideals in C*. As an inmediate consequence, Br C is a torsion group. Ž . Some cases where the map y * is an isomorphism are studied. It is also deduded from the main result that the inclusion of the coradical C into C induces a 0 Ž . Ž . monomorphism i#: Br C ª Br C . New examples of Brauer groups of cocom-0 mutative coalgebras may be given using this fact.

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The Irreducible Brauer Characters of the Finite Special Linear Groups in Non-describing Characteristics
✍ Jochen Gruber 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 357 KB

The irreducible Brauer characters of SL q are investigated for primes l not n Ž . dividing q. They are described in terms of a set of ordinary characters of SL q n whose reductions modulo l are a generating set of the additive group of generalized Brauer characters and the decomposition numbers of t