On the Brauer splitting theorem

Szeto, George

doi:10.2140/pjm.1969.31.505

Cited by 8 publications

(4 citation statements)

References 4 publications

(5 reference statements)

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“…As remarked in the discussion preceeding the proposition, (2) and (3) [18] and [21] characters T defined in such a way that they are in a one-to-one correspondence with the B i. (i)] is finitely generated, projective and separable over S. Now, suppose that R is a connected ring which does not split G, but GI U(R).…”

Section: Proofmentioning

confidence: 99%

More on the Schur group of a commutative ring

Mollin

1985

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring RG for some finite group G. It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur e:ponent f a ring which equals the well-known Schur index in the global or local field case.

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Section: Proofmentioning

confidence: 99%

More on the Schur group of a commutative ring

Mollin

1985

International Journal of Mathematics and Mathematical Sciences

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“…Then the group character T M :G-+R is defined by T M {g) = χ? =1 FiigX^ for any fir in G ( [8], §2).…”

Section: (A) Let R Be a Dedekind Domain And H = {J Such That P ~ φσFcmentioning

confidence: 99%

“…2); that is, RG ~ ©Σ?=i Hom R ,(P i9 Pi). Since R f is a local ring (see the proof of Theorem 2 in [8]) and P 4 is a finitely generated and projective R'-module for each i, P< is a free Jϊ'-module for each i ( [6], Th. 12 in Chapter 9).…”

Section: ί =mentioning

confidence: 99%

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The group character and split group algebras

Szeto¹

1970

Pacific J. Math.

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Applications of Frobenius Algebras to Representation Theory of Schur Algebras

Delvaux

Nauwelaerts

1998

Journal of Algebra

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A Schur algebra is a subalgebra of the group algebra RG associated to a partition of G, where G is a finite group and R is a commutative ring. For two classes of Schur algebras we study the relationship between indecomposable modules over the Schur algebra and over RG, but we discuss this problem in a more general context. Further we develop a character theory for Schur algebras; in particular, we express primitive central idempotents in terms of trace functions and we derive orthogonality relations for trace functions. These results are also presented in a more general context, namely for Frobenius algebras over rings. Moreover, we focus on class functions on Schur algebras.

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On the Brauer splitting theorem

Cited by 8 publications

References 4 publications

More on the Schur group of a commutative ring

More on the Schur group of a commutative ring

The group character and split group algebras

Applications of Frobenius Algebras to Representation Theory of Schur Algebras

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