Pre-lie Algebras and Incidence Categories of Colored Rooted Trees

Abstract

The incidence category CF of a family F of colored posets closed under disjoint unions and the operation of taking convex sub-posets was introduced by the author in [12], where the Ringel-Hall algebra HF of CF was also defined. We show that if the Hasse diagrams underlying F are rooted trees, then the subspace nF of primitive elements of HF carries a pre-Lie structure, defined over Z, and with positive structure constants. We give several examples of nF , including the nilpotent subalgebras of sln, Lgln, and several others.

Cite this paper

@inproceedings{Szczesny2010PrelieAA, title={Pre-lie Algebras and Incidence Categories of Colored Rooted Trees}, author={Matt Szczesny and Murray Gerstenhaber}, year={2010} }