4 papers · 1 filter
Faithful perversities
Alessio Cipriani, Jon Woolf
We show that the faithful highest weight hearts in an algebraic triangulated category are the serially faithful glued hearts, equivalently the hearts containing a dual pair of full…
Highest weight categories and stability conditions
Alessio Cipriani, Jon Woolf
Highest weight categories are an abstraction of the representation theory of semisimple Lie algebras introduced by Cline, Parshall and Scott in the late 1980s. There are by now man…
Simple tilts of length hearts and simple-minded mutation
Nathan Broomhead, Raquel Coelho Simoes, David Pauksztello +1
We characterise when a simple Happel-Reiten-Smalo tilt of a length heart is again a length heart in terms of approximation theory and the existence of a stability condition with a…
The heart fan of an abelian category
Nathan Broomhead, David Pauksztello, David Ploog +1
We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan.…