Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex

Luigi Alfonsi; Charles Young

doi:10.1016/j.geomphys.2023.104903

Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex

Luigi Alfonsi, Charles Young

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Abstract

The notion of a Manin triple of Lie algebras admits a generalization, to dg Lie algebras, in which various properties are required to hold only up to homotopy.

This paper introduces two classes of examples of such homotopy Manin triples. These examples are associated to analogs in complex dimension two of, respectively, the punctured formal 1-disc, and the complex plane with multiple punctures. The dg Lie algebras which appear include certain \emph{higher current algebras} in the sense of Faonte, Hennion and Kapranov.

We work in a ringed space we call rectilinear space, and one of the tools we introduce is a model of the derived sections of its structure sheaf, whose construction is in the spirit of the adelic complexes for schemes due to Parshin and Beilinson.

Original language	English
Article number	104903
Pages (from-to)	1-51
Number of pages	51
Journal	Journal of Geometry and Physics
Volume	191
Early online date	14 Jun 2023
DOIs	https://doi.org/10.1016/j.geomphys.2023.104903
Publication status	Published - 30 Sept 2023

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© 2023 The Author(s). Published by Elsevier B.V. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/
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Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex

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