Related papers: Half-flat structures on decomposable Lie groups

In this paper a characterisation is given of solvable complemented Lie algebras. They decompose as a direct sum of abelian subalgebras and their ideals relate nicely to this decomposition. The class of such algebras is shown to be a…

Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…

We introduce two nonnegative real-valued invariants for unital and stably finite C*-algebras whose minimal instances coincide with the notion of classifiability via the Elliott invariant. The first of these is defined for AH algebras, and…

The classification of graded non-alternating Hamiltonian Lie algebras over perfect field of characteristic 2 is obtained. It is shown that the filtered deformations of such algebras correspond to non-alternating Hamiltonian forms with…

The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution,…

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on Kaehler manifolds of the form M x SU(3)/H, with H = SU(2) x U(1) or H = U(1) x U(1). The induced rank two quiver gauge theories on M are worked out in detail for…

In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, K], then either…

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $\sigma$ be an involution of the…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

Non-alternating Hamiltonian Lie algebras in three variables over a perfect field of characteristic 2 are considered. A classification of non-alternating Hamiltonian forms over an algebra of divided powers in three variables and of the…

We study non-trivial deformations of the natural imbedding of the Lie algebra $\fh_1$ of lower triangular matrices (the Heisenberg Lie algebra) into $gl(3,\mathbb{K})$, where $\mathbb{K}=\mathbb{R}$ or $|mathbb{C}$. Our first result is the…

We study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined using the geometry of the Shilov boundary, Lie semigroup theory…

A finite-dimensional Lie algebra $L$ over a field $F$ is called an $A$-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an $A$-group: a finite group with the property that all of its Sylow…

A morphism Lie algebra is a triple $(\mathfrak{g}, \mathfrak{h}, \phi)$ consisting of two Lie algebras $\mathfrak{g}, \mathfrak{h}$ and a Lie algebra homomorphism $\phi : \mathfrak{g} \rightarrow \mathfrak{h}$. We define representations and…

We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…

We use the theory of dual of Fr\'echet-Schwartz (DFS) spaces to establish a sufficient condition for top-degree solvability for the differential complex associated to a hypocomplex locally integrable structure. As an application, we show…

A Lie conformal algebra is an algebraic structure that encodes the singular part of the operator product expansion of chiral fields in conformal field theory. A Lie pseudoalgebra is a generalization of this structure, for which the algebra…

We study the structure of the symplectic invariant part $\mathfrak{h}_{g,1}^{\mathrm{Sp}}$ of the Lie algebra $\mathfrak{h}_{g,1}$ consisting of symplectic derivations of the free Lie algebra generated by the rational homology group of a…

We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the first homology group of compact oriented surfaces.

We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show…