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The structure of the ladder insertion-elimination Lie algebra. (English) Zbl 1129.81060
Summary: We continue our investigation [Lett. Math. Phys. 67, No. 1, 61–74 (2004; Zbl 1081.17013)] into the insertion-elimination Lie algebra $$\mathcal L_L$$ 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 to the classical infinite dimensional Lie algebra $$\mathfrak Gl_+(\infty)$$ and we determine the cohomology of $$\mathcal L_L$$.

##### MSC:
 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 17B81 Applications of Lie (super)algebras to physics, etc. 81T18 Feynman diagrams
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