Published October 29, 2009 | Version Submitted
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The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra

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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.

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49875
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CaltechAUTHORS:20140919-164455687

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Funding

Defense Advanced Research Projects Agency (DARPA)
HR0011-09-1-0015

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Created
2014-09-22
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Updated
2023-06-02
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