Capability of Crossed Modules of Lie Algebras |
| |
Authors: | Behrouz Edalatzadeh |
| |
Institution: | 1. Department of Mathematics, Faculty of Science , Razi University , Kermanshah , Iran edalatzadeh@gmail.com |
| |
Abstract: | In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module. |
| |
Keywords: | Capability Cover of crossed modules Crossed module of Lie algebras Homology of crossed modules of Lie algebras |
|
|