Note on Complete Cohomology of a Quasi-Frobenius Algebra

Abstract

Let A be a quasi-Frobenius algebra over a field K. A has a complete (co)homology theory which may be established upon an augmented acyclic projective complex, i.e. a commutative diagram of A-double-modules with exact horizontal row, projective Xp, and with epimorphic resp. monomorphic ε and t. Negative-dimensional cohomology groups, over an A-double-module, are expected to be in close relationship with (ordinary positive-dimensional) homology groups.