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)

Last revised on August 18, 2023 at 22:42:01.
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