Stable endomorphism algebras of modules over special biserial algebras

By J. Schröer, Alexander Zimmermann. 2002

87 citations recorded by the source corpus.

Abstract. We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle algebra is gentle.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7f9df26fa804d3494dea358cb1e977df6a865444

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Citations in the corpus

Gentle algebras arising from surface triangulations (2009, background): “For instance, a once-punctured disc gives rise to cluster-tilted algebras of type D, see [29].”
Trivial extensions of gentle algebras and Brauer graph algebras (2014, background): “Both the classes of gentle algebras and that of Brauer graph algebras are special in the sense that they are closed under derived equivalence, see [25] for gentle algebras and [15] for Brauer graph algebras.”
The almost split triangles for perfect complexes over gentle algebras (2009, background): “if A is a gentle algebra and D(A) is equivalent as a triangulated category to D(B) for a finite dimensional algebra B, then B is also gentle [26].”
Singularity categories of gentle algebras (2012, background): “Examples of gentle algebras include tilted algebras of type An [1] and Ãn [2] and more generally all algebras which are derived equivalent to gentle algebras [20].”
Combinatorial derived invariants for gentle algebras (2006, background): “This class of algebras is closed under derived equivalence [17].”
A complete derived invariant for gentle algebras via winding numbers and Arf invariants (2019, background): “2 While it is assumed in [45] that the field k is algebraically closed, the proofs in that paper seems to be valid over any field.”
Discrete derived categories I: homomorphisms, autoequivalences and t-structures (2013, methodology): “on6.1means that the heart of each bounded t-structure in Db(( r;n;m)) is equivalent to mod(), for a nite-dimensional algebra of nite representation type. Note that, by work of Schroer and Zimmermann [41], is again gentle. Knowing this, we can now turn our attention solely to classifying the silting ”
A Geometric Model for the Module Category of a Gentle Algebra (2018, background): “gebra. Introduction Gentle algebras are an important class of ﬁnite dimensional algebras of tame representation type. Gentle algebras are Gorenstein [24], closed under tilting and derived equivalence [38, 39], and they are ubiquitous, for instance they occur in contexts such as Fukaya categories [27”