Categorification of a linear algebra identity and factorization of Serre functors

Details Categorification of a linear algebra identity and factorization of Serre functors Categorification of a linear algebra identity and factorization of Serre functors

2009-08-09

arxiv.org/abs/0908.1218v2

Mathematics

Representation Theory

18 pages; Minor changes, references added, new Section 2.7

Scientific paper

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.

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