Letters in Mathematical Physics

, Volume 102, Issue 2, pp 223–244

Integration of Lie 2-Algebras and Their Morphisms

Open Access


Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the integration procedure of Getzler and Henriques will also produce a 2-group. In this paper, we show that these two integration results are Morita equivalent. As an application, we integrate a non-strict morphism between Lie algebra crossed modules to a generalized morphism between their corresponding Lie group crossed modules.

Mathematics Subject Classification (2010)

Primary 17B55 Secondary 18B40 18D10 


L-algebras L-morphisms crossed modules Lie 2-groups Lie 2-algebras integration 


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of MathematicsJilin UniversityChangchunChina
  2. 2.Mathematischen Institut and Courant Research Centre “Higher Order Structures”University of GöttingenGöttingenGermany

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