The classification of \tau-tilting modules over Nakayama algebras

By T. Adachi. 2013

74 citations recorded by the source corpus.

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct the Hasse quiver of support tau-tilting modules by using Rejection Lemma of Drozd-Kirichenko.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a026cffa8eeb8ec39bd920e9023e1d9342b5ab79

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Lidia Angeleri Hugel
2. Sotaro Asai
3. C. Pfeifer

In Discrete Mathematics and Combinatorics

1. Lidia Angeleri Hugel
2. Sotaro Asai

In Geometry and Topology

1. Lidia Angeleri Hugel
2. Sotaro Asai
3. C. Pfeifer

Citations in the corpus

• Silting Objects (2018, methodology): “Then u and v can be used to construct a cohomological functor H0 t : T −→ Ht defined by H t (X) := u(v(X)[1]).”
• Semibricks (2016, background): “(2) For S0 ∈ S, a left mutation of X at S0 uniquely exists, and it is given as follows: – define a full subcategory E := FiltS0 of modA, – set YS0 := S0[1], – for any S ∈ S \ {S0}, take a left minimal E-approximation fS : S[−1] → ES in Db(modA) and define YS as the mapping cone of fS (we can see YS ”