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Title: Rhombus Filtrations and Rauzy Algebras.
Authors: Clark, Alex
Erdmann, Karin
Schroll, Sibylle
First Published: 3-Sep-2008
Publisher: Elsevier.
Citation: Bulletin des Sciences Mathématiques, 2009, 133 (1), pp. 56-81.
Abstract: Peach introduced rhombal algebras associated to quivers given by tilings of the plane by rhombi. We develop general techniques to analyze rhombal algebras, including a filtration by what we call rhombus modules. We introduce a way to relate the infinite-dimensional rhombal algebra corresponding to a complete tiling of the plane to finite-dimensional algebras corresponding to finite portions of the tiling. Throughout, we apply our general techniques to the special case of the Rauzy tiling, which is built in stages reflecting an underlying self-similarity. Exploiting this self-similar structure allows us to uncover interesting features of the associated finitedimensional algebras, including some of the tree classes in the stable Auslander-Reiten quiver.
DOI Link: 10.1016/j.bulsci.2008.08.006
ISSN: 0007-4497
Type: Article
Rights: This is the author’s final draft of the paper published as Bulletin des Sciences Mathématiques, 2009, 133 (1), pp. 56-81. The final published version is available at, Doi: 10.1016/j.bulsci.2008.08.006.
Appears in Collections:Published Articles, Dept. of Mathematics

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