Frobenius algebra

Summary

A Frobenius algebra is a finite-dimensional associative algebra over a field with a nondegenerate bilinear form that is compatible with the multiplication. Equivalently, the algebra is isomorphic to its own dual as a left module over itself. Group algebras of finite groups and matrix algebras are Frobenius algebras. Frobenius algebras are self-injective, and over them projective and injective modules coincide. Commutative Frobenius algebras also describe two-dimensional topological field theories.