The number of complete exceptional sequences for a Dynkin algebra

• Autorzy: Mustafa Obaid , Khalid Nauman , Wafa S. M. Al-Shammakh , Wafaa Fakieh , Claus Michael Ringel
• Języki publikacji: EN

Abstrakty

EN

The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.

Kategorie tematyczne

• 05A19: Combinatorial identities, bijective combinatorics
• 16G20: Representations of quivers and partially ordered sets
• 16G60: Representation type (finite, tame, wild, etc.)
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
• 05E10: Combinatorial aspects of representation theory
• 16G10: Representations of Artinian rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 2
• Strony: 197-210

Daty

wydano

2013

Twórcy

autor

Mustafa Obaid

• King Abdulaziz University, Faculty of Science, PO Box 80203, Jeddah 21589, Saudi Arabia

autor

Khalid Nauman

• King Abdulaziz University, Faculty of Science, PO Box 80200, Jeddah, Saudi Arabia

autor

Wafa S. M. Al-Shammakh

• King Abdulaziz University, Faculty of Science, PO Box 80200, Jeddah, Saudi Arabia

autor

Wafaa Fakieh

• King Abdulaziz University, Faculty of Science, PO Box 80200, Jeddah, Saudi Arabia

autor

Claus Michael Ringel

• King Abdulaziz University, Faculty of Science, PO Box 80200, Jeddah, Saudi Arabia

Identyfikatory

DOI

10.4064/cm133-2-6