Cluster-additive functions on stable translation quivers

Ringel CM (2012)
Journal of Algebraic Combinatorics 36(3): 475-500.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
Additive functions on translation quivers have played an important role in the representation theory of finite-dimensional algebras, the most prominent ones are the hammock functions introduced by S. Brenner. When dealing with cluster categories (and cluster-tilted algebras), one should look at a corresponding class of functions defined on stable translation quivers, namely the cluster-additive ones. We conjecture that the cluster-additive functions on a stable translation quiver of Dynkin type are non-negative linear combinations of cluster-hammock functions (with index set a tilting set). The present paper provides a first study of cluster-additive functions and gives a proof of the conjecture in the case .
Stichworte
Dynkin quiver; Cluster-hammocks; Hammocks; Cluster-additive function; Translation quiver; Additive function; Cluster-tilted algebra; Cluster category
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Algebraic Combinatorics
Band
36
Ausgabe
3
Seite(n)
475-500
ISSN
0925-9899
Page URI
https://pub.uni-bielefeld.de/record/2536052

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Ringel CM. Cluster-additive functions on stable translation quivers. Journal of Algebraic Combinatorics. 2012;36(3):475-500.
Ringel, C. M. (2012). Cluster-additive functions on stable translation quivers. Journal of Algebraic Combinatorics, 36(3), 475-500. doi:10.1007/s10801-012-0346-4
Ringel, C. M. (2012). Cluster-additive functions on stable translation quivers. Journal of Algebraic Combinatorics 36, 475-500.
Ringel, C.M., 2012. Cluster-additive functions on stable translation quivers. Journal of Algebraic Combinatorics, 36(3), p 475-500.
C.M. Ringel, “Cluster-additive functions on stable translation quivers”, Journal of Algebraic Combinatorics, vol. 36, 2012, pp. 475-500.
Ringel, C.M.: Cluster-additive functions on stable translation quivers. Journal of Algebraic Combinatorics. 36, 475-500 (2012).
Ringel, Claus Michael. “Cluster-additive functions on stable translation quivers”. Journal of Algebraic Combinatorics 36.3 (2012): 475-500.