Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-16T12:44:57.063Z Has data issue: false hasContentIssue false

On the Coxeter Transformations for Tamari Posets

Published online by Cambridge University Press:  20 November 2018

Frédéric Chapoton*
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 21 av Claude Bernard, F-69622 Villeurbanne Cedex, France e-mail: chapoton@math.univ-lyon1.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A relation between the anticyclic structure of the dendriform operad and the Coxeter transformations in the Grothendieck groups of the derived categories of modules over the Tamari posets is obtained.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Chapoton, F., On some anticyclic operads. Algebr. Geom. Topol. 5(2005), 5369.Google Scholar
[2] Friedman, H. and Tamari, D., Problèmes d’associativité: Une structure de treillis fini induite par une loi demi-associative. J. Combinatorial Theory 2(1967), 215242.Google Scholar
[3] Happel, D., Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, London Mathematical Society Lecture Note Series 119, Cambridge University Press, Cambridge, 1988.Google Scholar
[4] Hivert, F., Novelli, J.-C., and Thibon, J.-Y., The algebra of binary search trees. Theoret. Comput. Sci. 339(2005), no. 1, 129165.Google Scholar
[5] Lenzing, H., Coxeter transformations associated with finite-dimensional algebras. In: Computational Methods for Representations of Groups and Algebras, Progr. Math 173, Birkhäuser, Basel, 1999, pp. 287308.Google Scholar
[6] Loday, J.-L., Dialgebras. In: Dialgebras and Related Operads, Lecture Notes in Math. 1763, Springer, Berlin, 2001, pp. 766.Google Scholar
[7] Loday, J.-L. and Ronco, M. O., Hopf algebra of the planar binary trees. Adv. Math. 139(1998), no. 2, 293309.Google Scholar
[8] Loday, J.-L. and Ronco, M. O., Order structure on the algebra of permutations and of planar binary trees. J. Algebraic Combin. 15(2002), no. 3, 253270.Google Scholar
[9] Markl, M., Cyclic operads and homology of graph complexes. Rend. Circ. Mat. Palermo (2) Suppl. (1999), no. 59, 161170.Google Scholar
[10] Markl, M., Shnider, S., and Stasheff, J., Operads in Algebra, Topology and Physics. Mathematical Surveys and Monographs 96, American Mathematical Society, Providence, RI, 2002.Google Scholar
[11] Reading, N., Cambrian Lattices. Adv. Math. 205(2006), no. 2, 313353.Google Scholar
[12] Thomas, H., Tamari Lattices and Non-Crossing Partitions in Types B and D. arXiv:math.CO/0311334.Google Scholar