Wall and Chamber Structure for finite-dimensional Algebras

Abstract

We use $\tau$-tilting theory to give a description of the wall and chamber structure of a finite dimensional algebra. We also study $\mathfrak{D}$-generic paths in the wall and chamber structure of an algebra $A$ and show that every maximal green sequence in mod $A$ is induced by a $\mathfrak{D}$-generic path.

arXiv commentWe added Subsection 3.5 and corrected typos. This paper is a revised version of one part of a preprint arXiv:1705.08227

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• PBW parametrizations and generalized preprojective algebras
• Complete gentle and special biserial algebras are $g$-tame
• Pairwise Compatibility for 2-Simple Minded Collections II: Preprojective Algebras and Semibrick Pairs of Full Rank
• Stability over cDV singularities and other complete local rings
• The category of a partitioned fan
• Donaldson-Thomas invariants of length 2 flops
• Acyclic cluster algebras with dense $g$-vector fans
• From frieze patterns to cluster categories
• Lengths of maximal green sequences for tame path algebras
• Reduction Techniques to Identify Connected Components of Mutation Quivers
• Denseness of $g$-vector cones from weighted orbifolds
• Infinitesimal semi-invariant pictures and co-amalgamation
• The non-decreasing condition on g-vectors
• $\tau$-tilting finiteness and $\mathbf{g}$-tameness: Incidence algebras of posets and concealed algebras
• Relative left Bongartz completions and their compatibility with mutations