相关论文: The 4(th) structure

The co-Lie structures compatible with the osp(2|2) Lie super algebra structure are investigated and found to be all of coboundary type. The corresponding classical r-matrices are classified into several disjoint families. The osp(1|2)+u(1)…

The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore…

Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permutations. We are especially interested in cases when such…

The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a…

We make a four-algebraic extension of the IIB matrix model. The extension can be made by any Lie 4-algebra. The four-algebraic model has the same supersymmetry as the IIB matrix model, and hence as type IIB superstring theory. The…

We construct a convenient basis for all real semisimple Lie algebras by means of an adapted Chevalley basis of the complexification. It determines rational and in fact half-integer structure constants which we express only in terms of the…

We give a definition of quarternion Lie algebra and of the quarternification of a complex Lie algebra. By our definition gl(n,H), sl(n,H), so*(2n) and sp(n) are quarternifications of gl(n,C), sl(n,C), so(n,C) and u(n) respectively. Then we…

Four-dimensional, oriented Lie algebras $\mathfrak{g}$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $\mathfrak{g}$ are completely described. As a consequence, examples are given of…

In the present paper we shall investigate the Lie bialgebra structures on the Lie algebra $\widetilde{\frak{sl}_2(C_q[x,y])}$, which are shown to be triangular coboundary.

Lie bialgebras were introduced by Drinfeld in studying the solutions to the classical Yang-Baxter equation. The definition of a bialgebra in the sense of Drinfeld (D-bialgebra), related with any variety of algebras, was given by Zhelyabin.…

We classify all of the 4-dimensional linear Poisson structures of which the corresponding Lie algebras can be considered as the extension by a derivation of 3-dimensional unimodular Lie algebras. The affine Poisson structures on R^3 are…

All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.

Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of g and g^*. This description is then used to provide a…

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then its complexification has a hypercomplex structure. It is…

We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\em r-qn structures} on the corresponding Lie algebra $\mathfrak g$.…

In this work we deal with left invariant complex and symplectic structures on simply connected four dimensional solvable real Lie groups. We search the general form of such structures, when they exist and we make use of this information to…

We study a novel $n(n+1)/2$-dimensional non-semisimple Lie algebra $\mathfrak{g}_n$, a generalisation of both $\mathfrak{sl}_2(\mathbb{K})$ and the two-photon Lie algebra $\mathfrak{h}_6$. We investigate its properties, including its…

In this paper we classify all four dimensional real Lie bialgebras of symplectic type. The classical r- matrices for these Lie bialgebras and Poisson structures on all of the related four dimensional Poisson-Lie groups are also obtained.…

In this work we study a large class of exact Lie bialgebras arising from noncommutative deformations of Poisson-Lie groups endowed with a left invariant Riemannian metric. We call these structures \emph{exact metaflat Lie bialgebras}. We…