Cover of: The Schur subgroup of the Brauer group. | Toshihiko Yamada

The Schur subgroup of the Brauer group.

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Springer-Verlag , Berlin, New York
Finite groups, Representations of groups, Algebraic number t
SeriesLecture notes in mathematics, 397, Lecture notes in mathematics (Springer-Verlag) ;, 397.
Classifications
LC ClassificationsQA3 .L28 no. 397, QA171 .L28 no. 397
The Physical Object
Paginationiv, 159 p.
ID Numbers
Open LibraryOL5109135M
ISBN 100387068066
LC Control Number74181616

The Schur Subgroup of the Brauer Group. Authors: Yamada, T. Free Preview. Buy this book eB39 The schur subgroup of an imaginary field. Pages Yamada, Toshihiko. Book Title The Schur Subgroup of the Brauer Group Authors. Yamada; Series Title Lecture Notes in.

Schur algebras.- Cyclotomic algebras.- The brauer-witt theorem.- The schur subgroup of a p-adic field, p. The schur subgroup of a 2-adic field.- Properties of a schur algebra.- The schur subgroup of a real field.- The schur subgroup of an imaginary field.- Some theorems for a schur : T Yamada.

Description The Schur subgroup of the Brauer group. PDF

The Schur Subgroup of the Brauer Group. Authors; Toshihiko Yamada; Book. 59 Citations; Search within book. Front Matter. Pages I-V. PDF. Introduction. Toshihiko Yamada. Pages Schur algebras. Toshihiko Yamada. Pages The schur subgroup of a 2-adic field. Toshihiko Yamada.

Pages Properties of a schur algebra. Toshihiko. Schur algebras.- Cyclotomic algebras.- The brauer-witt theorem.- The schur subgroup of a p-adic field, p.

The schur subgroup of a 2-adic field.- Properties of a schur algebra.- The schur subgroup of a real field.- The schur subgroup of an imaginary field.- Some theorems for a schur algebra. Series Title.

Journals & Books; Register Sign in. Sign in Register. Journals & Books; Help; COVID campus closures: see options for getting or retaining Remote Access to subscribed content Vol Issue 3, DecemberPages The Schur subgroup of the Brauer group.

I Cited by: The Schur subgroup of the Brauer group consists of classes of k-central simple algebras that arise as simple components of group rings over k of finite groups. The projective Schur subgroup is obtained in a similar way but by allowing twisted group rings.

The projective Schur group relates to. The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford theory of finite groups. We show that the Schur-Clifford subgroup is indeed a subgroup of the Brauer-Clifford group, as are certain naturally defined subsets.

We also show that this Schur-Clifford subgroup behaves well with. The Schur Subgroup of the Brauer Group. II* TOSHIHIKO YAMADA Department of Mathematics, Tokyo Metropolitan University, Setagaya, Tokyo, Japan Communicated by W. Feit Received Septem This is a continuation of the previous paper [lo] and will determine the.

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Theorem A. IfZ≅Z(ϑ,κ,F)for some Clifford pair(ϑ,κ), thenSC(F)(G,Z)is a subgroup ofBrCliff(G,Z). With respect to the Brauer–Clifford group, the Schur–Clifford subgroup has the same rôle as the Schur subgroup [14]with respect to the Brauer group.

We will usually write SC(G,Z)instead of SC(F)(G,Z).Cited by: 1. The subgroup of the Schur subgroup generated by cyclic cyclotomic algebras Allen Herman, Gabriela Olteanu, Shmaia Angel del R´ıo´ Universidad de Murcia Alden Biesen, The Schur group K field Br(K) = Br(K) Brauer group of K = {[A]: A central simple K −algebra}.

Namely, G has a normal cyclic subgroup, the factor group G'/ is SCHUR SUBGROUP OF BRAUER GROUP. I isomorphic to ^, and f3 is exactly a factor set of the extension G or Cited by: The Schur Subgroup of the Brauer group. [Toshihiko Yamada] Book, Internet Resource: All Authors / Contributors: S.

Description: Seiten ; 8°. Contents: Schur algebras.- Cyclotomic algebras.- The brauer-witt theorem.- The schur subgroup of a p-adic field, p. The schur subgroup of a 2-adic field.- Properties of a schur. JOURNAL OF ALGE () The Schur Subgroup of the Brauer Group.

II* TOSHIHIKO YAMADA Department of Mathematics, Tokyo Metropolitan University, Setagaya, Tokyo, Japan Communicated by W. Feit Received Septem INTRODUCTION This is a continuation of the previous paper [10] and will determine the Schur subgroups of some real cyclotomic fields, using the Cited by:   Yamada T.

() The schur subgroup of the brauer group. In: Proceedings of the Conference on Orders, Group Rings and Related Topics. Lecture Notes in Mathematics, vol Cited by: SCHUR SUBGROUP OF BRAUER GROUP.

1 isomorphic to 3, and /3 is exactly a factor set of the extension G of ({j by 9. Since G spans B with coefficients in k, B is k-isomorphic to a simple com- ponent of kG. In particular, the class [B] is in the Schur subgroup S(k). Additional Physical Format: Online version: Yamada, Toshihiko, Schur subgroup of the Brauer group.

Berlin, New York, Springer-Verlag, (OCoLC) The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford theory of finite groups.

We show that the Schur-Clifford subgroup is indeed a subgroup of the Brauer-Clifford group, as are certain naturally defined subsets. We also show that this Schur-Clifford subgroup behaves well with. Cite this chapter as: Yamada T.

() The schur subgroup of a p-adic field, p≠2. In: The Schur Subgroup of the Brauer Group. Lecture Notes in Mathematics, vol Cited by: 4. The Schur group of is the subgroup of the Brauer group consisting of those classes of centrally simple -algebras that occur in the group algebra of some finite group.

Since the Schur indices for are trivial in prime characteristic (Wedderburn's theorem; cf. also Schur index), one may assume that. By Brauer's theorem (cf. Schur index), the field of th roots of unity is a splitting field for. The Schur subgroup S(k) of the Brauer group JS(k) consists of those algebra classes which contain a simple component of the group algebra kG for some finite group G.

If A is a central simple algebra over k, then [A] will denote the class of A in JS(k).Cited by:   We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group, similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford theory of finite groups.

We show that the Schur-Clifford subgroup is indeed a subgroup of the Brauer-Clifford group, as are certain naturally defined Cited by: 1. The Schur subgroup of the Brauer group. [Toshihiko Yamada] Home.

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classes which contain a simple component of the group algebra kG for some finite group G. If A is a central simple algebra over k, then [A] will denote the class of A in B(K).

The Schur subgroup was first investigated by K. Fields and I. Herstein [5]. Since the elements of the Brauer group.

The Schur subgroup of the Brauer group. By Toshihiko Yamada. Download PDF ( KB) Cite. BibTex; Full citation; Publisher: Published by Elsevier Inc. Year: DOI identifier: /(73) OAI identifier: Provided by: Elsevier - Publisher Connector.

Downloaded Author: Toshihiko Yamada. Genre/Form: Electronic books: Additional Physical Format: Print version: Yamada, Toshihiko, Schur subgroup of the Brauer group.

Berlin, New York, Springer-Verlag. H-projective Schur subgroup represents classes of Azumaya R-algebras which are epimorphic image of a twisted group algebra R∗ α Gfor some G∈ H. Restricting to the case where only the trivial cocycle appears we obtain the H-Schur subgroup.

On the other hand, the Brauer group of a cocommutative coalgebra C was introduced in [15]. The Brauer group is always a subgroup of the cohomological Brauer group. Gabber showed that the Brauer group is equal to the cohomological Brauer group for any scheme with an ample line bundle (for example, any quasi-projective scheme over a commutative ring).

2 CHAPTER IV. THE BRAUER GROUP PROPOSITION Let Abe an Azumaya algebra over R. Then Ahas center R; moreover, for any ideal3 JofA, JD.J\R/A, and for any ideal Iof R, \R. Thus J7!J\R is a bijection from the ideals of Ato those of R.

˚be an endomorphism of Aas an ˚is multiplication by an. Cite this chapter as: Yamada T. () The brauer-witt theorem. In: The Schur Subgroup of the Brauer Group. Lecture Notes in Mathematics, vol Then the Schur subgroup of the Brauer group is defined, in analogy with, via representations of finite groups on finitely generated projective -modules.

It is easy to see that. We shall show that there is equality in the case of a purely cyclotomic extension of (where is an th root of 1). We write B(k) for the Brauer group of k, and Bn(k) for the subgroup of B(k) generated by classes of division rings of exponent n.

Let S(k) be the subgroup of B(k) consisting of all classes which contain a simple component of QfG], the group algebra of a finite group G over the rational field Q.

Following [6] we call S(k) the Schur subgroup of k.We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group, similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup contains exactly the equivalence classes.If k is a field, the projective Schur group PS(k) of k is the subgroup of the Brauer group Br(k) consisting of those classes which contain a projective Schur algebra, i.e., a homomorphic image of.