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

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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 languageEnglish
Article number104903
Pages (from-to)1-51
Number of pages51
JournalJournal of Geometry and Physics
Volume191
Early online date14 Jun 2023
DOIs
Publication statusPublished - 30 Sept 2023

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