Published September 22, 2014
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The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra
- Creators
- Zhu, Xinwen
Abstract
For any abelian category C satsifying (AB5) over a separated, quasi-compact scheme S, we construct a stack of 2-groups GL(C) over the flat site of S. We will give a concrete description of GL(C) when C is the category of quasi-coherent sheaves on a separated, quasi-compact scheme X over S. We will show that the tangent space gl(C) of GL(C) at the origin has a structure as a Lie 2-algebra.
Additional Information
Imported from arXiv. Supported by DARPA through the grant HR0011-09-1-0015. This paper was motivated by my joint project with Edward Frenkel [FZ1, FZ2] on gerbal representations of double groups and Lie algebras. I would like to express my deep gratitude to him for collaboration and numerous discussions. I would also like to thank Martin Olsson and Chenyang Xu for useful discussions.Attached Files
Submitted - 0910.5699v1.pdf
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Additional details
- Eprint ID
- 49875
- Resolver ID
- CaltechAUTHORS:20140919-164455687
- HR0011-09-1-0015
- Defense Advanced Research Projects Agency (DARPA)
- Created
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2014-09-22Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field