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Wall-and-chamber structures for finite-dimensional algebras and -tilting theory
Maximilian Kaipel, Hipolito Treffinger
The wall-and-chamber structure is a geometric invariant that can be associated to any algebra. In this notes we give the definition of this object and we explain its relationship w…
A geometric perspective on the -cluster morphism category
Sibylle Schroll, Aran Tattar, Hipolito Treffinger +1
We show how the -cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that t…
Stability spaces of string and band modules
Sibylle Schroll, Aran Tattar, Hipolito Treffinger +2
The stability space of a module is the cone of vectors which make the module semistable. These cones are defined in terms of inequalities; in this paper we draw insights from consi…
Extending (-)tilting subcategories and (co)silting modules
J. Asadollahi, F. Padashnik, S. Sadeghi +1
Let be a finite dimensional algebra and be the one-point extension algebra of with respect to the finitely generated projective -module . The categories…
On -tilting subcategories
Javad Asadollahi, Somayeh Sadeghi, Hipolito Treffinger
The main theme of this paper is to study -tilting subcategories in an abelian category with enough projective objects. We introduce the notion of -cotorsion tor…