Authors: Jon F. Carlson and Peter Webb
Title: The Graded Center of a Triangulated Category
Abstract:
With applications in mind to the representations and cohomology
of block algebras, we examine elements of the graded center of
a triangulated category when the category has a Serre functor.
These are natural transformations from the identity functor to
powers of the shift functor that commute with the shift functor
We show that such natural transformations which have support in
a single shift orbit of indecomposable objects are necessarily
of a kind previously constructed by Linckelmann. Under further
conditions, when the support is contained in only finitely many
shift orbits, sums of transformations of this special kind
account for all possibilities.
Allowing infinitely many shift orbits in the support, we construct
elements of the graded center of the stable module category of
a tame group algebra of a kind that cannot occur with wild block algebras.
We use functorial methods extensively in the proof, developing some
of this theory in the context of triangulated categories.
Status: Preprint August 2015.