Related papers: Symmetric Lie models of a triangle

This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…

We prove that a 2-step nilpotent Lie algebras admitting an ad-invariant metric can be constructed from a vector space $\mathfrak v$ endowed with a inner product $<, >$ and an injective homomorphism $\rho: \mathfrak v \to…

Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$…

We propose a construction of the spherical subalgebra of a symplectic reflection algebra of an arbitrary rank corresponding to a star-shaped affine Dynkin diagram. Namely, it is obtained from the universal enveloping algebra of a certain…

In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…

We construct families of $k$-step nilpotent symplectic Lie algebras associated with graphs, extending the construction given in [Pouseele-Tirao, JPAA 213 (2009)] for the 2-step case. We also show that, under mild conditions on the…

We generalize the notion of kinematical Lie algebra introduced in physics for the classification of the various possible relativity algebras an isotropic spacetime can accommodate. We first give an elementary proof of the fact that such a…

Let $\Gamma$ be a metric graph having a linear system $g^r_{2r}$ for some $2 \leq r \leq g-2$ then $\Gamma$ has a linear system $g^1_2$. This is similar to the well-known Clifford's Theorem from the theory of linear systems on smooth…

We have discovered that the gauge invariant observables of matrix models invariant under U($N$) form a Lie algebra, in the planar large-N limit. These models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We study here…

A map $\phi$ on an associative ring is called a multiplicative Lie derivation if $\phi([x,y])=[\phi(x),y]+[x,\phi(y)]$ holds for any elements $x,y$, where $[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative Lie…

We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $…

Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…

The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are motivated…

The Lie sphere geometry is a natural extension of the M\"obius geometry, where the latter is very important in string theory and the AdS/CFT correspondence. The extension to Lie sphere geometry is applied in the following to a sequence of…

Using tight binding model, lattice QFT and group theory methods, we study a class of lattice QFT models that are cousins of graphene; and which are classified by finite dimensional ADE Lie groups containing the usual crystallographic…

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established…

Let G be a n-dimensional Lie group (n>2) with a bi-invariant Riemannian metric. We prove that if a surface of constant Gaussian curvature in G can be expressed as the product of two curves, then it must be flat. In particular, we can…

Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials…

The Higman--Thompson groups $V_{n,r}$ consist of piecewise linear automorphisms of $r$ intervals where cut points and slopes are $n$-adic. Szymik and Wahl prove homological stability for this family of groups as $r$ increases, and compute…