Related papers: Stepwise Square Integrability for Nilradicals of P…

We determine fundamental systems of invariants for complex solvable rigid Lie algebras having nonsplit nilradicals of characteristic sequence $(3,1,..,1)$, these algebras being the natural followers of solvable algebras having Heisenberg…

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation preserving homeomorphisms of the unit interval with finitely many breaks in slope, and also subgroups of Thompson's group F. We find geometric criteria…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive…

We study nonnegative solutions to the following Hardy-H\'enon type equations involving higher order fractional Laplacians $$ (-\Delta)^\sigma u = |x|^{-\alpha}u^{p} ~~~~~~ \mbox{in} ~ \mathbb{R}^n \backslash \{0\} $$ with a possible…

Consider $\mathbb R^d\times \mathbb R^m$ with the group structure of a two-step nilpotent Lie group and natural parabolic dilations. The maximal function originally introduced by Nevo and Thangavelu in the setting of the Heisenberg group…

Let {\Lnk} be the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideals. In 2020 the authors et al. gave a classification of all non 2-step nilpotent Lie algebras of {\Li}. We propose in this paper to…

In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Lie groups equipped with left invariant metrics. As applications, we get a spinorial proof of the Fundamental Theorem for submanifolds…

We show that any subgroup of a (virtually) nilpotent-by-polycyclic group satisfies the bounded packing property of Hruska-Wise. In particular, the same is true about metabelian groups and linear solvable groups. However, we find an example…

Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution…

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…

We show that every non-compact simple real Lie algebra not isomorphic to so(n,1) has a unique conjugacy class of parabolic subalgebras whose nilradical is of Heisenberg type, or non-singular, and give some applications.

We consider left-invariant (purely) coclosed G$_2$-structures on 7-dimensional 2-step nilpotent Lie groups. According to the dimension of the commutator subgroup, we obtain various criteria characterizing the Riemannian metrics induced by…

In this paper we provide the final steps in the proof, announced by Eskin-Fisher-Whyte, of quasi-isometric rigidity of a class of non-nilpotent polycyclic groups. To this end, we prove a rigidity theorem on the boundaries of certain…

The central concept in the harmonic analysis of a compact group is the completeness of Peter-Weyl orthonormal basis as constructed from the matrix coefficients of a maximal set of irreducible unitary representations of the group, leading…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

We give a complete classification of irreducible symmetric spaces for which there exist proper SL(2,R)-actions as isometries, using the criterion for proper actions by T. Kobayashi [Math. Ann. '89] and combinatorial techniques of nilpotent…

We conjecture an integrability and linearizability test for dispersive Z^2-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation…

Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak n$ the nilradical of a parabolic subalgebra of $\mathfrak g$. We consider some properties of the coadjoint representation of $\mathfrak n$ and related algebras of invariants.…