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The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra

Zhu, Xinwen (2009) The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra. . (Submitted)

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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.

Item Type:Report or Paper (Discussion Paper)
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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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Defense Advanced Research Projects Agency (DARPA)HR0011-09-1-0015
Record Number:CaltechAUTHORS:20140919-164455687
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49875
Deposited By: George Porter
Deposited On:22 Sep 2014 19:35
Last Modified:03 Oct 2019 07:18

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