Tensor products of nonassociative cyclic algebras

TL;DR

This paper investigates when the tensor product of an associative and a nonassociative cyclic algebra forms a division algebra, extending classical results and exploring applications in space-time block coding.

Contribution

It generalizes classical division algebra conditions to mixed associative and nonassociative cases and discusses specific conditions and applications.

Findings

Tensor product is a division algebra under classical conditions with roots of unity.

Stronger conditions are identified in special cases.

Applications to space-time block coding are explored.

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.