nLab quasi-Frobenius algebra

Definition

Recall that an algebra is a Frobenius algebra if its left regular representation $L(A)$ is isomorphic to its right regular representation $R(A)$. For quasi-Frobenius algebras, this isomorphism is weakened.

Definition

An algebra $A$ is called a quasi-Frobenius algebra if the isomorphism classes of idecomposable components of its left-regular representation $L(A)$ matches those of its right-regular representation $R(A)$.

References

The notion of quasi-Frobenius algebras (first?) appears in

• Tadasi Nakayama. On Frobeniusean Algebras. I. Annals of Mathematics, Second Series, Vol. 40, No. 3 (Jul., 1939), pp. 611-633 (23 pages). (doi)