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.
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 | |
Publication status | Published - 30 Sept 2023 |