Related papers: Harmonic morphisms from the classical non-compact …

We construct a new family of curvature homogeneous pseudo-Riemannian manifolds modeled on $\mathbb{R}^{3k+2}$ for integers $k \geq 1$. In contrast to previously known examples, the signature may be chosen to be $(k+1+a, k+1+b)$ where $a,b…

We study all four-dimensional simply-connected indecomposable non-semisimple pseudo-Riemannian symmetric spaces whose metric has signature (2,2). We present models and compute their isometry groups. We solve the problem of the existence or…

Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved…

This is a challenging paper including some review and new results. Since the non-commutative version of the classical system based on the compact group SU(2) has been constructed in (quant-ph/0502174) by making use of Jaynes-Commings model…

We consider a compact Lie group as a framed manifold equipped with the left invarianat framing $\mathscr{L}$. In a previous paper we have proved that the Adams $e_\mathbb{C}$-invariant value of $SU(2n)$ $(n\ge 2)$ gives a generator of the…

Spherically symmetric solutions of the SU(N) Einstein-Yang-Mills-Higgs system are constructed using the harmonic map ansatz. The problem reduces to solving a set of ordinary differential equations for the appropriate profile functions. In…

We construct many examples of Lie groups with compact Levi factor admitting a left-invariant metric with negative Ricci curvature. We start with a Lie algebra with Levi factor su(n) or so(n) acting on an abelian nilradical via the…

Over a field of characteristic p > 2, the first cohomology of the special linear Lie superalgebra sl(2,1) with coefficients in all \c{hi}-reduced Kac modules and simple modules is determined by use of the weight space decompositions of…

In this article, we mainly obtain the Riemann-Hurwitz theorems for harmonic morphisms on (vertex-weighted) metric graphs or metrized complexes of algebraic curves, inspired of the recent work on harmonic morphisms of graphs or metrized…

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M|N), can give interesting anomaly-free sets of fermion representations of SU(M) x SU(N) x U(1). It is shown here that such groups can…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $sp(n,1)$. Our choice of these algebras is motivated by the fact that they belong to a…

In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the…

Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).

Let $G$ be a connected, simply connected one-parameter metabelian nilpotent Lie group, that means, the corresponding Lie algebra has a one-codimensional abelian subalgebra. In this article we show that $G$ contains a discrete cocompact…

We prove that the automorphism group of a compact 6-manifold $M$ endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min$\{5,b_1(M)\}$. Moreover, we study the properties of the automorphism…

We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie algebras up to dimension four and all six-dimensional…

Approaches to calculate SU(N) colored knot invariants (HOMFLY-PT polynomials) are well and widely developed. However, SO(N) case is mostly forgotten. With this paper we want to start the discusion of how to generalize Reshetikhin-Turaev…

We prove that SU(n) (n > 2) and Sp(n)U(1) (n > 1) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group.…

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications…

The unit sphere $\mathbb S^3$ can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vector fields of the corresponding…