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Reduction and reconstruction of multisymplectic Lie systems
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, ...
Lie algebroids arising from simple group schemes
(Academic Press Inc Elsevier Science, 2017-10)
A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within ...
Torsors, reductive group schemes and extended affine Lie algebras
(American Mathematical Society, 2013-11)
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction ...
The distribution of symmetry of a naturally reductive nilpotent Lie group
(Springer, 2019-06)
We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact ...
On conjugacy of Cartan subalgebras in extended affine Lie algebras
(Academic Press Inc Elsevier Science, 2016-02)
That finite-dimensional simple Lie algebras over the complex numbers can be classified by means of purely combinatorial and geometric objects such as Coxeter-Dynkin diagrams and indecomposable irreducible root systems, is ...
The index of symmetry of three-dimensional Lie groups with a left-invariant metric
(De Gruyter, 2018-10)
We determine the index of symmetry of 3-dimensional unimodular Lie groups with a left-invariant metric. In particular, we prove that every 3-dimensional unimodular Lie group admits a left-invariant metric with positive ...
A Lie algebra approach to Lie group time integration of constrained systems
(Springer International Publishing, 2016)
Lie group integrators preserve by construction the Lie group structure of a nonlinear configuration space. In multibody dynamics, they support a representation of (large) rotations in a Lie group setting that is free of ...
On the Isometry Groups of Invariant Lorentzian Metrics on the Heisenberg Group
(Birkhauser Verlag Ag, 2014-01)
This work concerns the invariant Lorentzian metrics on the Heisenberg Lie group of dimension three H3(R) and the bi-invariant metrics on the solvable Lie groups of dimension four. We start with the indecomposable Lie groups ...
Naturally reductive pseudo-riemannian 2-step nilpotent lie groups
(University of Houston, 2013-01)
This paper deals with naturally reductive pseudo-Riemannian 2- step nilpotent Lie groups for which the metric is invariant under a left action. The case of nondegenerate center is characterized as follows. The simply ...
On distinguished orbits of reductive representations
(Elsevier, 2013-12)
Let G be a real reductive Lie group and let τ : G −→ GL(V ) be a real reductive representation of G with (restricted) moment map mg : V {0} −→ g. In this work, we introduce the notion of nice space of a real reductive ...