A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras
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...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Netherlands
2018
|
| Online Access: | http://hdl.handle.net/1721.1/118298 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826199791529361408 |
|---|---|
| author | Enriquez, Benjamin Etingof, Pavel I |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Enriquez, Benjamin Etingof, Pavel I |
| author_sort | Enriquez, Benjamin |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:25:50Z |
| format | Article |
| id | mit-1721.1/118298 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:25:50Z |
| publishDate | 2018 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1182982022-10-01T03:35:10Z A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras Enriquez, Benjamin Etingof, Pavel I Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I 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. National Science Foundation (U.S.) (Grant DMS-1502244) 2018-10-01T14:19:43Z 2018-10-01T14:19:43Z 2017-12 2018-09-19T03:55:20Z Article http://purl.org/eprint/type/JournalArticle 1386-923X 1572-9079 http://hdl.handle.net/1721.1/118298 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. https://orcid.org/0000-0002-0710-1416 en https://doi.org/10.1007/s10468-017-9754-4 Algebras and Representation Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer Science+Business Media B.V., part of Springer Nature application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Enriquez, Benjamin Etingof, Pavel I A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title | A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title_full | A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title_fullStr | A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title_full_unstemmed | A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title_short | A Tannakian Interpretation of the Elliptic Infinitesimal Braid Lie Algebras |
| title_sort | tannakian interpretation of the elliptic infinitesimal braid lie algebras |
| url | http://hdl.handle.net/1721.1/118298 https://orcid.org/0000-0002-0710-1416 |
| work_keys_str_mv | AT enriquezbenjamin atannakianinterpretationoftheellipticinfinitesimalbraidliealgebras AT etingofpaveli atannakianinterpretationoftheellipticinfinitesimalbraidliealgebras AT enriquezbenjamin tannakianinterpretationoftheellipticinfinitesimalbraidliealgebras AT etingofpaveli tannakianinterpretationoftheellipticinfinitesimalbraidliealgebras |