Related papers: Canonical almost pseudo-K\"{a}hler structures on s…

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and…

For a torsion free finitely generated nilpotent group G we naturally associate four finite dimensional nilpotent Lie algebras over a field of characteristic zero. We show that if G is a relatively free group of some variery of nilpotent…

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex…

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on…

We study the examples mentioned in [2,Tables A & C] and establish the arithmeticity of four examples of symplectic hypergeometric groups of degree six. Following [2] we know that there are 458 inequivalent symplectic hypergeometric groups…

In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of…

We give a complete classification of left invariant generalized complex structures of type 1 on four dimensional simply connected Lie groups and we compute for each class its invariant generalized Dolbeault cohomology, its invariant…

Let $G$ be a Lie group of even dimension and let $(g,J)$ be a left invariant anti-K\"ahler structure on $G$. In this article we study anti-K\"{a}hler structures considering the distinguished cases where the complex structure $J$ is abelian…

Working over an arbitrary field of characteristic different from $2$, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension $4$. In case the base…

Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly K\"ahler manifolds is provided.

Every symplectic Lie algebra with degenerate (including non-abelian nilpotent symplectic Lie algebras) has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding…

For a closed smooth manifold $M$ admitting a symplectic structure, we define a smooth topological invariant $Z(M)$ using almost-K\"ahler metrics, i.e. Riemannian metrics compatible with symplectic structures. We also introduce $Z(M,…

We study symplectic structures on nilpotent Lie algebras. Since the classification of nilpotent Lie algebras in any dimension seems to be a crazy dream, we approach this study in case of 2-step nilpotent Lie algebras (in this sub-case also,…

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

We study Lie algebras of generators of infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. The almost-cosymplectic-contact structure admits on the sheaf of pairs of 1-forms and functions the…

Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable…

It has been known that there exist exactly three left-invariant Lorentzian metrics up to scaling and automorphisms on the three dimensional Heisenberg group. In this paper, we classify left-invariant Lorentzian metrics on the direct product…

Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential…

We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and…