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Baez and Crans in their paper on Lie 2-algebras refer to adjoint representations of Lie 2-groups but don't say much, as far as I can tell, except to say that such a representation acts on a 2-Lie algebra. Where can I find a description of the adjoint representation of Lie 2-groups?

Is there any connection with representations of Lie groupoids up to homotopy?

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  • $\begingroup$ I guess Baez and Crans say "Lie 2-algebras," so I have edited the question. I couldn't find the definition of an adjoint representation in the arxiv.org/abs/math/0409602, just a brief comment that it exists and no reference. That's one of the reasons for posing the question. $\endgroup$
    – Eugene Lerman
    Commented Aug 16, 2014 at 18:54
  • $\begingroup$ See also page 6 in arxiv.org/pdf/1306.6225v1.pdf on the adjoint representation. $\endgroup$
    – Dietrich Burde
    Commented Aug 16, 2014 at 21:28
  • $\begingroup$ p. 6 of arxiv.org/pdf/1306.6225v1.pdf talks about adjoint representations of Lie 2-algebras not of Lie 2-groups. $\endgroup$
    – Eugene Lerman
    Commented Aug 17, 2014 at 11:20
  • $\begingroup$ I had once thought on this. IMHO, there is no adjoint representation of Lie 2-groups unless for strict Lie 2-groups (cross module). $\endgroup$
    – Ma Ming
    Commented Oct 12, 2016 at 8:58
  • $\begingroup$ @Ma Ming So what's the adjoint rep of Lie crossed modules? $\endgroup$
    – Eugene Lerman
    Commented Oct 12, 2016 at 17:06

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