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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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