Projective Schur Division Algebras Are Abelian Crossed Products

Eli Aljadeff; Jack Sonn

doi:10.1006/jabr.1994.1044

Projective Schur Division Algebras Are Abelian Crossed Products

Eli Aljadeff, Jack Sonn

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Abstract

Let k be a field. A projective Schur Algebra over k is a finite-dimensional k-central simple algebra which is a homomorphic image of a twisted group algebra k^αG with G a finite group and α ∈ H²(G, k*). The main result of this paper is that every projective Schur division algebra is an abelian crossed product (K/k, f(hook)), where K is a radical extension of k.

Original language	English
Pages (from-to)	795-805
Number of pages	11
Journal	Journal of Algebra
Volume	163
Issue number	3
DOIs	https://doi.org/10.1006/jabr.1994.1044
State	Published - 1 Feb 1994
Externally published	Yes

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title = "Projective Schur Division Algebras Are Abelian Crossed Products",

abstract = "Let k be a field. A projective Schur Algebra over k is a finite-dimensional k-central simple algebra which is a homomorphic image of a twisted group algebra kαG with G a finite group and α ∈ H2(G, k*). The main result of this paper is that every projective Schur division algebra is an abelian crossed product (K/k, f(hook)), where K is a radical extension of k.",

author = "Eli Aljadeff and Jack Sonn",

year = "1994",

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doi = "10.1006/jabr.1994.1044",

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N2 - Let k be a field. A projective Schur Algebra over k is a finite-dimensional k-central simple algebra which is a homomorphic image of a twisted group algebra kαG with G a finite group and α ∈ H2(G, k*). The main result of this paper is that every projective Schur division algebra is an abelian crossed product (K/k, f(hook)), where K is a radical extension of k.

AB - Let k be a field. A projective Schur Algebra over k is a finite-dimensional k-central simple algebra which is a homomorphic image of a twisted group algebra kαG with G a finite group and α ∈ H2(G, k*). The main result of this paper is that every projective Schur division algebra is an abelian crossed product (K/k, f(hook)), where K is a radical extension of k.

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JO - Journal of Algebra

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Projective Schur Division Algebras Are Abelian Crossed Products

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