Higher Morita-Tachikawa correspondence (Q6593639)

The Morita-Tachikawa correspondence connects basic finite-dimensional algebras having dominant dimension at least two with pairs consisting of a basic finite-dimensional algebra and a multiplicity-free generator-cogenerator.\N\NIn the paper, the author introduces the concepts of $n$-quasi-generators and $n$-quasi-cogenerators that generalise generators and cogenerators, respectively, where $n$ is a non-negative integer. Using these new concepts, the author presents higher versions of the Morita-Tachikawa correspondence that take into account relative dominant dimension with respect to a self-orthogonal module with arbitrary projective and injective dimensions. These new versions also hold over Noetherian algebras that are finitely generated and projective over a commutative Noetherian ring.