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Abstract
In this article, we give a sufficient condition for a Lie color algebra to be complete. The color derivation algebra Der(ℋ) and the holomorph L of finite dimensional Heisenberg Lie color algebra ℋ graded by a torsion-free abelian group over an algebraically closed field of characteristic zero are determined. We prove that Der(ℋ) and Der(L) are simple complete Lie color algebras, but L is not a complete Lie color algebra.
ACKNOWLEDGMENTS
The authors are indebted to the referee for his/her providing the detailed comments and suggestions, which helped us improve the earlier version.
Yang is supported by NNSFC (Grants: 11026037), Science & Technology Program of Shanghai Maritime University, Hu is supported in part by the NNSFC (Grants: 10971065, 10728102), the PCSIRT and the RFDP from the MOE, the National & Shanghai Leading Academic Discipline Projects (Project Number: B407).
Notes
Communicated by K. Misra.