Susanne Pumpluen

Skew polynomials, nonassociative algebras, and their applications

Using skew polynomial rings, we define a class of unital nonassociative algebras introduced by Petit in 1966 but still basically unknown. Some of these algebras are canonical - nonassociative - generalizations of (associative) central simple algebras. Classical results from Albert, Amitsur and Jacobson can be generalized to this nonassociative setting. Our algebras can be used in space-time block coding, to get maximum rank distance codes and in deciding when a skew polynomial is reducible. Their most prominent feature is that their right nucleus is the eigenspace of the skew polynomial used it their construction.