The Structure of the Ladder Insertion-Elimination Lie algebra
Igor Mencattini, Dirk Kreimer
TL;DR
This paper explores the structure and cohomology of the ladder insertion-elimination Lie algebra related to Feynman graphs, aiming to inform future research on Dyson-Schwinger equations.
Contribution
It analyzes the algebra's relation to classical infinite-dimensional Lie algebras and determines its cohomology, advancing understanding of its mathematical properties.
Findings
Relation to classical infinite-dimensional Lie algebras established
Cohomology of the ladder insertion-elimination Lie algebra computed
Insights provided for applications in Dyson-Schwinger equations
Abstract
We continue our investigation into the insertion-elimination Lie algebra of Feynman graphs in the ladder case, emphasizing the structure of this Lie algebra relevant for future applications in the study of Dyson-Schwinger equations. We work out the relation of this Lie algebra to some classical infinite dimensional Lie algebra and we determine its cohomology.
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