Algebras and Representation Theory

, Volume 14, Issue 1, pp 75–77

Appendix to Cluster-Cyclic Quivers with Three Vertices and the Markov Equation, by A. Beineke, Th. Brűstle and L. Hille

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Abstract

The relation between the Markov constant of an acyclic cluster algebra of rank 3 and the dimension of the first Hochschild cohomology group of the corresponding hereditary algebra will be shown.

Keywords

Cluster algebras Clustertilted algebras Hochschild cohomology Markov constant 

Mathematics Subject Classifications (2000)

16G20 16E40 

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References

  1. 1.
    Buan, A., Marsh, R., Reiten, I.: Cluster mutations via quiver representations. arXiv: math.RT/0412077 (2004)
  2. 2.
    Happel, D.: Hochschild cohomology of finite-dimensional algebras. In: Sem. M.P. Malliavin, Springer Lect. Notes Math., vol. 1404, pp. 108–126 (1989)Google Scholar
  3. 3.
    Lukas, F.: Elementare moduln über wilden erblichen algebren. Thesis, Düsseldorf (1992)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Mathematisches InstitutHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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