Cohomology and deformations of 3-Lie colour algebras

Abstract

In this paper, we introduce the concept of -Lie colour algebras which is a generalization of -Lie algebras. The cohomology theory of 3-Lie colour algebras is developed. The deformations of 3-Lie colour algebras are considered via the cohomology theory. We also study the abelian extensions of 3-Lie colour algebras in details.

Keywords:

• 3-Lie colour algebras
• cohomology
• deformations
• Nijenhuis operators
• abelian extensions

AMS Subject Classifications:

• 17A40
• 17B75
• 17B56

Acknowledgements

The author would like to thank the referee for careful reading of the paper and for valuable comments which helped to improve this paper significantly. The last section and many references were added under the referee’s suggestions. Part of this work was done while the author was visiting Courant Research Centre, Georg-August Universität Göttingen from June to September, 2013. He is grateful to the University of Göttingen for hospitality and financial support.