Tensor products of nonassociative cyclic algebras

Pumpluen, Susanne

Abstract

We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or Jacobson, if the base field contains a suitable root of unity. Stronger conditions are obtained in special cases. Applications to space–time block coding are discussed.

Citation

Pumpluen, S. (2016). Tensor products of nonassociative cyclic algebras. Journal of Algebra, 451, https://doi.org/10.1016/j.jalgebra.2015.12.007

• Journal Article Type: Article
• Acceptance Date: Dec 16, 2015
• Online Publication Date: Dec 22, 2015
• Publication Date: Apr 1, 2016
• Deposit Date: Jun 21, 2016
• Publicly Available Date: Jun 21, 2016
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 0021-8693
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 451
• DOI: https://doi.org/10.1016/j.jalgebra.2015.12.007
• Keywords: cyclic algebra, nonassociative cyclic algebra, nonassociative quaternion algebra, tensor product, division algebra
• Public URL: https://nottingham-repository.worktribe.com/output/778014
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0021869315006213