Letters in Mathematical Physics

, Volume 102, Issue 2, pp 223–244

Integration of Lie 2-Algebras and Their Morphisms

Authors

  • Yunhe Sheng
    • Department of MathematicsJilin University
    • Mathematischen Institut and Courant Research Centre “Higher Order Structures”University of Göttingen
Open AccessArticle

DOI: 10.1007/s11005-012-0578-1

Cite this article as:
Sheng, Y. & Zhu, C. Lett Math Phys (2012) 102: 223. doi:10.1007/s11005-012-0578-1

Abstract

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 17B55Secondary 18B4018D10

Keywords

L-algebrasL-morphismscrossed modulesLie 2-groupsLie 2-algebrasintegration
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Copyright information

© The Author(s) 2012