The Brauer group of dimodule algebras

Long, Fred

doi:10.1016/0021-8693(74)90224-5

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Introduction3

There Is a Contravariant Functor1

Preliminaries1

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1991

2005

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Cited by 83 publications

(44 citation statements)

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“…The category of such modules and A-linear C-colinear morphisms is called the category of Long dimodules, denoted by L C A , and was introduce by F. Long in [Lon74]. Considering A as a trivial R-comodule algebra and C as a trivial right R-module coalgebra we get the right-right Doi-Koppinen structure (R, A, C) and it follows that…”

Section: There Is a Contravariant Functormentioning

confidence: 99%

Dual Entwining Structures and Dual Entwined Modules

Abuhlail

2005

Algebr Represent Theor

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Section: There Is a Contravariant Functormentioning

confidence: 99%

Dual Entwining Structures and Dual Entwined Modules

Abuhlail

2005

Algebr Represent Theor

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“…These two groups belong to the classical theory of the Brauer group of an abelian group. See [4], [9], [10]. The Brauer group BM(k, * as Hopf algebras.…”

Section: Preliminariesmentioning

confidence: 99%

The Brauer Group of the Dihedral Group

Carnovale¹,

Cuadra

2004

Glasgow Math. J.

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Abstract. Let p m be a power of a prime number p, ‫ބ‬ p m be the dihedral group of order 2p m and k be a field where p is invertible and containing a primitive 2p m -th root of unity. The aim of this paper is computing the Brauer group BM(k, ‫ބ‬ p m , R z ) of the group Hopf algebra of ‫ބ‬ p m with respect to the quasi-triangular structure R z arising from the group Hopf algebra of the cyclic group ‫ޚ‬ p m of order p m , for z coprime with p.

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“…Long dimodules are the building stones of the Brauer-Long group, in the case where the Hopf algebra H is commutative, cocommutative and faithfully projective (see [7], and [1] for a detailed discussion). Long dimodules are also connected to a non-linear equation (see [9]).…”

Section: Introductionmentioning

confidence: 99%