Generalized Benson-Carlson duality (Q1911326)

This paper examines the results of \textit{D. J. Benson} and \textit{J. F. Carlson} [Trans. Am. Math. Soc. 342, No. 2, 447-488 (1994; Zbl 0816.20044)] and analyzes what happens if the complexes \(C_\zeta\) of that paper are replaced by arbitrary Yoneda extensions representing \(\zeta\). The setting is that of the homological algebra of a finite dimensional cocommutative Hopf algebra \(\Lambda\) over an algebraically closed field \(k\) in which the \(k\)-algebra \(\text{Ext}^*_\Lambda(k,k)\) is finitely generated and for any f.g. \(\Lambda\)-modules \(M\) and \(N\), \(\text{Ext}_\Lambda^*(M,N)\) is finitely generated as an \(\text{Ext}^*_\Lambda(k,k)\)-module.