The numbers of support-tilting modules for a Dynkin algebra

Abstract

The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper exhibits the number of support-tilting modules for any Dynkin algebra. Since the support-tilting modules for a Dynkin algebra correspond bijectively to the non-crossing partitions of the same type, the calculations presented here may also be considered as a categorification of results concerning non-crossing partitions.

The presentation has been improved, the proof of Corollary 16 has been corrected. The previous versions included an appendix with a proof of the Ingalls-Thomas bijections for general hereditary artin algebras; it has been deleted and will be published separately

References in corpus (1)

• Universal derived equivalences of posets of tilting modules

Cited by in corpus (2)

• Tilting Modules over the Path Algebra of Type A, Polytopes, and Catalan Numbers
• Some applications of $\tau$-tilting theory