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Rhombus Filtrations and Rauzy Algebras.

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journal contribution
posted on 28.01.2009, 11:22 by Alex Clark, Karin Erdmann, Sibylle Schroll
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.

History

Citation

Bulletin des Sciences Mathématiques, 2009, 133 (1), pp. 56-81.

Published in

Bulletin des Sciences Mathématiques

Publisher

Elsevier.

issn

0007-4497

Copyright date

2009

Available date

28/01/2009

Publisher version

http://www.sciencedirect.com/science/article/pii/S0007449708000687

Language

en

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