Related papers: Symmetric Lie models of a triangle

An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…

In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an $L_\infty$-algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie $3$-algebra…

We consider (smooth) solutions of the mean curvature flow of graphs over bounded domains in a Lie group free up to step two (and not necessarily nilpotent), endowed with a one parameter family of Riemannian metrics $\sigma_\e$ collapsing to…

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 give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.

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 index of symmetry. We…

We call a connected Lie group endowed with a left-invariant Lorentzian flat metric Lorentzian flat Lie group. In this Note, we determine all Lorentzian flat Lie groups admitting a timelike left-invariant Killing vector field. We show that…

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The…

In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we…

In the companion paper arXiv:2110.05298, we developed the deformation theory of symplectic foliations, focusing on geometric aspects. Here, we address some algebraic questions that arose naturally. We show that the $L_{\infty}$-algebra…

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field…

We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical Wess-Zumino-Witten model. We…

Classical mechanical systems are modeled by a symplectic manifold $(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on $M$ by diffeomorphisms that preserves $\omega$. These actions, which are called "symplectic",…

We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to…

We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups,…

Here we present a theory of mirror-symmetric magic angle twisted trilayer graphene. The electronic properties are described by a Hubbard model with long range tunneling matrix elements. The electronic properties are obtained by solving the…