A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras
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Author(s)
Enriquez, Benjamin
Etingof, Pavel I
Date Issued
December 2017
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Citation
Enriquez, Benjamin, and Pavel Etingof. “A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras.” Algebras and Representation Theory, vol. 21, no. 5, Oct. 2018, pp. 943–1002.
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Author's final manuscript
Abstract
Let n ≥ 1. The pro-unipotent completion of the pure braid group of n points on a genus 1 surface has been shown to be isomorphic to an explicit pro-unipotent group with graded Lie algebra using two types of tools: (a) minimal models (Bezrukavnikov), (b) the choice of a complex structure on the genus 1 surface, making it into an elliptic curve E, and an appropriate flat connection on the configuration space of n points in E (joint work of the authors with D. Calaque). Following a suggestion by P. Deligne, we give an interpretation of this isomorphism in the framework of the Riemann-Hilbert correspondence, using the total space E[superscript #] of an affine line bundle over E, which identifies with the moduli space of line bundles over E equipped with a flat connection.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s10468-017-9754-4
