5 citations · 13 across the 8 of their papers we have counts for
8 papers
Preprojective roots of Coxeter groups
Mark Kleiner
Certain results on representations of quivers have analogs in the structure theory of general Coxeter groups. A fixed Coxeter element turns the Coxeter graph into an acyclic quiver…
Adjoint Functors, Projectivization, and Differentiation Algorithms for Representations of Partially Ordered Sets
Mark Kleiner, Markus Reitenbach
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal poin…
Preprojective representations of valued quivers and reduced words in the Weyl group of a Kac-Moody algebra
Mark Kleiner, Allen Pelley
This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each pre…
Sequences of reflection functors and the preprojective component of a valued quiver
Mark Kleiner, Helene R. Tyler
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geo…
Admissible sequences, preprojective modules, and reduced words in the Weyl group of a quiver
Mark Kleiner, Allen Pelley
This paper studies connections between the preprojective modules over the path algebra of a finite connected quiver without oriented cycles, the (+)-admissible sequences of vertice…
Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank
Steven P. Diaz, Mark Kleiner
With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal…