Geodesic
The number of complete exceptional sequences for a Dynkin algebra
Mustafa Obaid 1   ; Khalid Nauman 2   ; Wafa S. M. Al-Shammakh 2   ; Wafaa Fakieh 2   ; Claus Michael Ringel 2
1 King Abdulaziz University Faculty of Science PO Box 80203 Jeddah 21589, Saudi Arabia
2 King Abdulaziz University Faculty of Science PO Box 80200 Jeddah, Saudi Arabia
Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 197-210 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\varDelta $ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type $\varDelta $, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
DOI : 10.4064/cm133-2-6
Keywords: dynkin algebras hereditary artin algebras finite representation type paper determines number complete exceptional sequences dynkin algebra since complete exceptional sequences dynkin algebra dynkin type vardelta correspond bijectively maximal chains lattice non crossing partitions type vardelta calculations presented here may considered categorification corresponding result non crossing partitions

Mustafa Obaid  1   ; Khalid Nauman  2   ; Wafa S. M. Al-Shammakh  2   ; Wafaa Fakieh  2   ; Claus Michael Ringel  2

1 King Abdulaziz University Faculty of Science PO Box 80203 Jeddah 21589, Saudi Arabia
2 King Abdulaziz University Faculty of Science PO Box 80200 Jeddah, Saudi Arabia 
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Mustafa Obaid; Khalid Nauman; Wafa S. M. Al-Shammakh; Wafaa Fakieh; Claus Michael Ringel. The number of complete exceptional sequences
 for a Dynkin algebra. Colloquium Mathematicum, Tome 133 (2013) no. 2, pp. 197-210. doi: 10.4064/cm133-2-6

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