Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebras
Lo\"ic Foissy (LM-Reims)
TL;DR
This paper explores the structure of prelie algebras through left ideals in enveloping algebras and modules, ultimately proving that most simple complex Lie algebras are not prelie, except possibly F4.
Contribution
It provides a new characterization of prelie algebras using left ideals and modules, and establishes a significant non-existence result for simple complex Lie algebras.
Findings
Most simple complex Lie algebras are not prelie
F4 may be an exception
New characterization of prelie algebras
Abstract
We characterize prelie algebras in words of left ideals of the enveloping algebras and in words of modules, and use this result to prove that a simple complex finite-dimensional Lie algebra is not prelie, with the possible exception of f4.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology