  A self-dual algebras is one isomorphic as a module to the opposite of its
dual; a quasi self-dual algebra is one whose cohomology with coefficients in
itself is isomorphic to that with coefficients in the opposite of its dual. For
these algebras, cohomology with coefficients in itself, which governs its
deformation theory, is a contravariant functor of the algebra. Finite
dimensional self-dual algebras over a field are identical with symmetric
Frobenius algebras. (The monoidal category of commutative Frobenius algebras is
known to be equivalent to that of 1+1 dimensional topological quantum field
theories.) All finite poset algebras are quasi self-dual.
