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Frobenius algebras are finite-dimensional algebras together with a compatible inner product. Commutative Frobenius algebras have attracted recent interest because they're equivalent to 2D oriented TQFTs.

3 votes

A non-example of a graded Frobenius algebra

A pretty trivial example is an algebra with the zero product. Less trivial is $k[x,y]/(x,y)^2$ where $x$ has degree $1$ and $y$ has degree $2$. One can make up various similar examples, e.g., $k[x,y,z …
Zach Teitler's user avatar
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2 votes

Reference on the classification of (low rank) Gorenstein rings over $\mathbb{C}$

This paper might possibly be relevant: http://www.ams.org/mathscinet-getitem?mr=2922602 It's not quite exactly what you are asking for. Instead of Gorenstein algebras of low rank, they are consideri …
Zach Teitler's user avatar
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