Classification of three dimensional complex Leibniz algebras

Rikhsiboev, Ikrom M.; Rakhimov, Isamiddin S.
May 2012
AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p358
Academic Journal
The aim of this paper is to complete the classification of three-dimensional complex Leibniz algebras. The description of isomorphism classes of three-dimensional complex Leibniz algebras has been given by Ayupov and Omirov in 1999. However, we found that this list has a little redundancy. In this paper we apply a method which is more elegant and it gives the precise list of isomorphism classes of these algebras. We compare our list with that of Ayupov-Omirov and show the corrections which should be made.


Related Articles

  • Q kink of the nonlinear O(3) σ model involving an explicitly broken symmetry. Loginov, A. // Physics of Atomic Nuclei;May2011, Vol. 74 Issue 5, p740 

    The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S,...

  • On a Class of Representations of the Yangian and Moduli Space of Monopoles. Gerasimov, A.; Kharchev, S; Lebedev, D.; Oblezin, S. // Communications in Mathematical Physics;Dec2005, Vol. 260 Issue 3, p511 

    A new class of infinite dimensional representations of the Yangians Y and Y corresponding to a complex semisimple algebra and its Borel subalgebra is constructed. It is based on the generalization of the Drinfeld realization of in terms of quantum minors to the case of an arbitrary semisimple...

  • Local Currents for a Deformed Heisenberg–Poincaré Lie Algebra of Quantum Mechanics, and Anyon Statistics. Goldin, Gerald A.; Sarkar, Sarben // International Journal of Theoretical Physics;Feb2008, Vol. 47 Issue 2, p297 

    We set out to construct a Lie algebra of local currents whose space integrals, or “charges”, form a subalgebra of the deformed Heisenberg–Poincaré algebra of quantum mechanics discussed by Vilela Mendes, parameterized by a fundamental length scale ℓ. One possible...

  • Gell-Mann formula for simple complex Lie groups and geometric quantization. Šťovíček, P. // Journal of Mathematical Physics;Jun88, Vol. 29 Issue 6, p1300 

    A Lie–Poisson isomorphism for Lie algebras [ATOTHER]@Fg[/ATOTHER] and [ATOTHER]@Fq[/ATOTHER] =[ATOTHER]@Fk[/ATOTHER] ×[ATOTHER]@Fk[/ATOTHER] is derived in a closed form, where [ATOTHER]@Fg[/ATOTHER] is complex and simple, and [ATOTHER]@Fk[/ATOTHER] is the maximal compact subalgebra in...

  • Lie algebras with complex structures having nilpotent eigenspaces. LICURGO SANTOS, EDSON CARLOS; SAN MARTIN, LUIZ A. B. // Proyecciones - Journal of Mathematics;2011, Vol. 30 Issue 2, p247 

    Let (g, [�,�]) be a Lie algebra with an integrable complex structure J. The �i eigenspaces of J are complex subalgebras of gC isomorphic to the algebra (g, [*]J) with bracket [X * Y]J = � ([X,Y ] - [JX,JY]). We consider here the case where these subalgebras are nilpotent and...

  • Isomorphism classes and invariants for a subclass of nine-dimensional filiform Leibniz algebras. Deraman, F.; Rakhimov, I. S.; Husain, S. K. Said // AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p326 

    The paper concerns the classification problem of a subclass of nilpotent Leibniz algebras. This subclass arises from naturally graded non Lie filiform Leibniz algebras. An invariant-theoretic approach to the classification problem of this subclass has been suggested by Rakhimov and Bekbaev. This...

  • Classification of abelian complex structures on 6-dimensional Lie algebras. Andrada, A.; Barberis, M. L.; Dotti, I. // Journal of the London Mathematical Society;Feb2011, Vol. 83 Issue 1, p232 

    We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parametrize, on each of these algebras, the space of such structures up to holomorphic isomorphism.

  • Some Results on Equivalence Groups. Ndogmo, J. C. // Journal of Applied Mathematics;2012, p1 

    The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite...

  • Remarks on A[sub 2] Toda Theory. Apikyan, S. A.; Efthimiou, C. J. // JETP Letters;12/25/2001, Vol. 74 Issue 12, p569 

    We study the Toda field theory with finite Lie algebras using an extension of the Goulian�Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting correlation function resembles that of a free theory....


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics