Lengths of maximal green sequences for tame path algebras

Ryoichi Kase; Ken Nakashima

doi:10.1007/s40687-021-00290-3

Lengths of maximal green sequences for tame path algebras

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Abstract

In this paper, we study the maximal length of maximal green sequences for quivers of type D~ and E~ by using the theory of tilting mutation. We show that the maximal length does not depend on the choice of the orientation and determine it explicitly. Moreover, we give a program which counts all maximal green sequences by length for a given Dynkin/extended Dynkin quiver.

Original language	English
Article number	59
Journal	Research in Mathematical Sciences
Volume	8
Issue number	4
DOIs	https://doi.org/10.1007/s40687-021-00290-3
Publication status	Published - Dec 2021
Externally published	Yes

Keywords

(τ-)tilting theory
Maximal green sequence
Quiver representation
Support (τ-)tilting poset
Tame path algebra

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)
Computational Mathematics
Applied Mathematics

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10.1007/s40687-021-00290-3

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AB - In this paper, we study the maximal length of maximal green sequences for quivers of type D~ and E~ by using the theory of tilting mutation. We show that the maximal length does not depend on the choice of the orientation and determine it explicitly. Moreover, we give a program which counts all maximal green sequences by length for a given Dynkin/extended Dynkin quiver.

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KW - Maximal green sequence

KW - Quiver representation

KW - Support (τ-)tilting poset

KW - Tame path algebra

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ER -

Lengths of maximal green sequences for tame path algebras

Abstract

Keywords

ASJC Scopus subject areas

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