Categorification of a linear algebra identity and factorization of Serre functors
arXiv:0908.1218 · doi:10.1007/s00209-016-1731-9
Abstract
We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre functor of a finite dimensional triangular algebra A has always a lift, up to shift, to a product of suitably defined reflection functors in the category of perfect complexes over the trivial extension algebra of A.
arXiv comment18 pages; Minor changes, references added, new Section 2.7