Tensor products of nonassociative cyclic algebras

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.

Final version, contains additional information on how to use the investigated algebras to build fast-decodable fully diverse space-time block codes; to appear in Journal of Algebra

References in corpus (2)

• The nonassociative algebras used to build fast-decodable space-time block codes
• A Fast Decodable Full-Rate STBC with High Coding Gain for 4x2 MIMO Systems

Cited by in corpus (5)

• The nonassociative algebras used to build fast-decodable space-time block codes
• Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma ,\delta )$-codes
• Nonassociative cyclic extensions of fields and central simple algebras
• How a nonassociative algebra reflects the properties of a skew polynomial
• Quotients of orders in algebras obtained from skew polynomials with applications to coding theory