Title of article :
THE INGALLS-THOMAS BIJECTIONS
Author/Authors :
A. A. Obaid, Mustafa King Abdulaziz University - Faculty of Science, Saudi Arabia , Nauman, S. Khalid King Abdulaziz University - Faculty of Science, Saudi Arabia , Fakieh, Wafaa M King Abdulaziz University - Faculty of Science, Saudi Arabia , Michael Ringel, Claus King Abdulaziz University - Faculty of Science, Saudi Arabia
Abstract :
Given a finite acyclic quiver Q with path algebra Λ, Ingalls and
Thomas have exhibited a bijection between the set of Morita equivalence
classes of support-tilting modules and the set of thick subcategories of mod Λ
with covers, and they have collected further bijections with these sets. We add
some additional bijections and show that all these bijections hold for arbitrary
hereditary artin algebras. The proofs presented here seem to be of interest
also in the special case of the path algebra of a quiver.
Keywords :
Tilting module , support-tilting module , thick subcategory , normal module , conormal module , torsion pair , antichain , exceptional antichain
Journal title :
International Electronic Journal of Algebra
