Loading...

Crossed product conditions for central simple algebras in terms of irreducible subgroups

Keshavarzipour, T ; Sharif University of Technology | 2007

115 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.jalgebra.2007.05.002
  3. Publisher: 2007
  4. Abstract:
  5. Let Mm (D) be a finite dimensional F-central simple algebra. It is shown that Mm (D) is a crossed product over a maximal subfield if and only if GLm (D) has an irreducible subgroup G containing a normal abelian subgroup A such that CG (A) = A and F [A] contains no zero divisor. Various other crossed product conditions on subgroups of D* are also investigated. In particular, it is shown that if D* contains either an irreducible finite subgroup or an irreducible soluble-by-finite subgroup that contains no element of order dividing deg (D)2, then D is a crossed product over a maximal subfield. © 2007 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Division ring ; Crossed product ; Irreducible groups
  8. Source: Journal of Algebra ; Volume 315, Issue 2 , 2007 , Pages 738-744 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0021869307002748