PRODUCT STRUCTURES ON FOUR DIMENSIONAL SOLVABLE LIE ALGEBRAS

By Adrián Andrada, M. L. Barberis, I. Dotti, G. Ovando. 2004

114 citations recorded by the source corpus.

It is the aim of this work to study product structures on four dimensional solvable Lie algebras. We determine all possible paracomplex structures and consider the case when one of the subalgebras is an ideal. These results are applied to the case of Manin triples and complex product structures. We also analyze the three dimensional subalgebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a97a9cf0090005a490bbccefdbb869ccd94452d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. G. Ovando

In Geometry and Topology

1. Dmitri Alekseevsky
2. C. Medori
3. Adriano Tomassini
4. G. Ovando
5. Adrián Andrada
6. S. Salamon

In Mathematical Physics

1. Dmitri Alekseevsky
2. C. Medori
3. Adriano Tomassini
4. G. Ovando
5. Adrián Andrada
6. S. Salamon

Citations in the corpus

• Homogeneous para-Kähler Einstein manifolds (2009, background): “Many other interesting examples of left-invariant hypersymplectic structures of solvable Lie groups had been given in [15], [18] , [17] and [ 16 ], where all such structures on 4-dimensional Lie groups had been classified.”
• Realizations of real low-dimensional Lie algebras (2003, background): “nd results concerning this problem, which were adduced in the previous papers of G.M. Mubarakzyanov [49], F. Bratzlavsky [8], G.I. Kruchkovich and A.Z. Petrov [27, 62], Patera et al [58]. In preprint [2] authors reproduced the classification of four-dimensional real Lie algebras and compared their re”
• Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures (2016, unknown): “Moreover, for b 6= 0, gb is isomorphic to r4,1/b,−1/2b and g0 is isomorphic to r4,− 1 2 ,− 1 2 from [2], and it follows that they are not pairwise isomorphic for b ≥ 0.”
• Four dimensional symplectic Lie algebras (2004, methodology): “The second sequence (11) splits (see [2]) and so we prove that g is a generalized symplectic double extension.”