Nonassociative algebras and applications

Project description

Nonassociative algebras can be investigated over rings, fields, or algebraic varieties. Their algebra structure, i.e. the multiplication, is given by a bilinear map. In other words, the multiplication is not required to be associative anymore, as it is usually the case when one talks about algebras. Techniques for investigating certain classes of nonassociative algebras (e.g. octonion algebras) include for instance applying results from number theory and elementary algebraic geometry.

Recently some work has been focusing on understanding algebras over nonarchimedean local rings, and their potential applications.

Nonassociative algebras can be employed in coding theory, for instance to construct maximum rank distance codes, or space-time block codes.

There are lots of interesting open problems in this area, both easier and very difficult ones.