Related papers: Segre varieties and Lie symmetries

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.

We give a complete classification, up to isometric isomorphism and scaling, of $4$-dimensional metric Lie algebras $(\mathfrak{g},\langle \cdot,\cdot \rangle)$ that admit a non-zero parallel skew-symmetric endomorphism. In particular, we…

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…

For every parabolic subgroup $P$ of a Lie supergroup $G$, the homogeneous superspace $G/P$ carries a $G$-invariant supergeometry. We address the question whether $\mathfrak{g}=\text{Lie}(G)$ is the maximal supersymmetry of this…

We generalize a result of Serre's to show that if every vertex of some fixed type of a convex subcomplex of an irreducible spherical building has an opposite, then the subcomplex is completely reducible.

We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…

Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the…

We describe how to smoothly parametrize certain families of nilpotent Lie algebras.

Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…

A fundamental property of Segre classes is their birational invariance. This invariance implies that the Segre class of a closed subscheme only depends on the integral closure of the defining ideal sheaf. In this paper, we show that,…

We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\"acklund…

We describe a computational proof that the fifth secant variety of the Segre product of five copies of the projective line is a codimension 2 complete intersection of equations of degree 6 and 16. Our computations rely on pseudo-randomness,…

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…

The set HLie(n) of the n-dimensional Hom-Lie algebras over an algebraically closed field of characteristic zero is provided with a structure of algebraic subvariety of the affine plane of dimension n^2(n-1)/2}. For n=3, these two sets…

We describe the parametric behavior of the series solutions of an A-hypergeometric system. More precisely, we construct explicit stratifications of the parameter space such that, on each stratum, the series solutions of the system are…

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…

This paper is devoted to geodesic completeness of left-invariant metrics for real and complex Lie groups. We start by establishing the Euler-Arnold formalism in the holomorphic setting. We study the real Lie group $\mathrm{SL}(2,…

We compute the dimensions of all the secant varieties to the tangential varieties of all Segre-Veronese surfaces. We exploit the typical approach of computing the Hilbert function of special 0-dimensional schemes on projective plane by…

This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the…

Segre-Veronese manifolds are smooth submanifolds of tensors comprising the partially symmetric rank-1 tensors. We investigate a one-parameter family of warped geometries of Segre-Veronese manifolds, which includes the standard Euclidean…