A class of real solvable lie algebras such that their k-orbits are orbits of zero or four dimensions

Le Anh Vu * , Duong Quang Hoa , & Nguyen Anh Tuan

* Correspondence: Le Anh Vu (email: 420_leanhvu@gmail.com)

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Received: 10 Jan 2014
Revised: 10 Feb 2014
Accepted: 10 Feb 2014
Published: 15 Mar 2014
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Lê, V. A., Dương, H. Q., & Nguyễn, T. A. (2014). A class of real solvable lie algebras such that their k-orbits are orbits of zero or four dimensions. Van Hien University Journal of Science (2), 33-37.
Issue
Issue 2 (2014)
Section
Cong Nghe

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Abstract

In this paper, classification of MD-algebras by maximal dimension of orbit in the co-adjoint representation firstly used by Arnal-Cahen-Ludwig in [1], we introduce a subclass of MD-algebras such that maximal-dimensional orbit is 4 in co-adjoint representation.

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References

1. Arnal D., Cahen M., Ludwig J. (1995), "Lie Groups whose Coadjoint orbits are of Dimension Smaller or Equal to Two', Kluwer Academic Publishers, Netherlands, 33, 183-186.

2. Vu L.A. (1990), "On the Foliations Formed by the Generic K-orbits of the MD4-Groups", Acta Math. Vietnam, NO 2, 39-55.

3. Vu L.A., Shum K.P. (2008), "Classification of 5-dimensional MD-algebra having commutative derived ideals", Advances in Algebra and Combinatorics, Singapore: World Scientific co, 353-371.

4. Vu L.A., Hoa D.Q. (2009), "The topology of foliations formed by the generic K-orbits of a subclass of the indecomposable MD5groups, Science in China, series A: Mathemmatics, 52 (2), 351-360.

5. Vu L.A., Hieu H.V., Nghia T.T.H. (2011), "Classification of 5-Dimensional MD-algebras Having Non-commutative Derived Ideals", East-West Journal of Mathematics, Volume 13, No 2, pp. 115-129.