Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Universal enveloping crossed module of a Lie crossed module

Pages: 143 – 158

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a7

Authors

José Manuel Casas (Department of Applied Mathematics I, University of Vigo, Pontevedra, Spain)

Rafael F. Casado (Department of Algebra, University of Santiago de Compostela, Spain)

Emzar Khmaladze (A. Razmadze Mathematical Institute, Tbilisi State University, Tbilisi, Georgia; and Department of Applied Mathematics I, University of Vigo, Pontevedra, Spain)

Manuel Ladra (Department of Algebra, University of Santiago de Compostela, Spain)

Abstract

We construct a pair of adjoint functors between the categories of crossed modules of Lie and associative algebras, which extends the classical one between the categories of Lie and associative algebras. This result is used to establish an equivalence of categories of modules over a Lie crossed module and its universal enveloping crossed module.

Keywords

crossed module, Lie algebra, associative algebra, universal enveloping algebra

2010 Mathematics Subject Classification

16W25, 16W99, 17B35, 18A40

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