The Number of Support-Tilting Modules for a Dynkin Algebra
Mustafa A. A. Obaid, S. Khalid Nauman, Wafaa M. Fakieh, and Claus Michael Ringel
King Abdulaziz University
P. O. Box 80200
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 of Dynkin type Δ correspond bijectively to the
generalized non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of results
concerning the generalized non-crossing partitions. In the Dynkin
case A, we obtain the Catalan triangle, in the cases B
and C the
increasing part of the Pascal triangle, and finally in the case D an
expansion of the increasing part of the Lucas triangle.
Full version: pdf,
(Concerned with sequences
January 5 2015;
revised versions received September 7 2015; September 18 2015.
Published in Journal of Integer Sequences, September 24 2015.
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