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Journal Article

Quantum L∞ algebras and the homological perturbation lemma

MPS-Authors
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Jurčo,  Branislav
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1712.02696.pdf
(Preprint), 425KB

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Citation

Doubek, M., Jurčo, B., & Pulmann, J. (2019). Quantum L∞ algebras and the homological perturbation lemma. Communications in Mathematical Physics, 367(1), 215-240. doi:10.1007/s00220-019-03375-x.


Cite as: http://hdl.handle.net/21.11116/0000-0004-F015-5
Abstract
Quantum $L_\infty$ algebras are a generalization of $L_\infty$ algebras with a scalar product and with operations corresponding to higher genus graphs. We construct a minimal model of a given quantum $L_\infty$ algebra via the homological perturbation lemma and show that it's given by a Feynman diagram expansion, computing the effective action in the finite-dimensional Batalin-Vilkovisky formalism. We also construct a homotopy between the original and this effective quantum $L_\infty$ algebra.