# On The Structure and Representations of the Insertion–Elimination Lie Algebra

@article{Szczesny2008OnTS,
title={On The Structure and Representations of the Insertion–Elimination Lie Algebra},
author={M. Szczesny},
journal={Letters in Mathematical Physics},
year={2008},
volume={84},
pages={65-74}
}
• M. Szczesny
• Published 2008
• Mathematics
• Letters in Mathematical Physics
We examine the structure of the insertion–elimination Lie algebra on rooted trees introduced in Connes and Kreimer (Ann. Henri Poincar 3(3):411–433, 2002). It possesses a triangular structure $${\mathfrak{g} = \mathfrak{n}_+ \oplus \mathbb{C}\cdot d \oplus \mathfrak{n}_-}$$ , like the Heisenberg, Virasoro, and affine algebras. We show in particular that it is simple, which in turn implies that it has no finite-dimensional representations. We consider a category of lowest-weight representations… Expand
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