Related papers: Moufang loops with commuting inner mappings

Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…

Recently it was shown that the scaling dimension of the operator $\phi^n$ in scale-invariant $d=3$ theory may be computed semiclassically, and this was verified to leading order (two loops) in perturbation theory at leading and subleading…

We explore the possibilities for elementary embeddings $j : M \to N$, where $M$ and $N$ are models of ZFC with the same ordinals, $M \subseteq N$, and $N$ has access to large pieces of $j$. We construct commuting systems of such maps…

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…

We prove that if the multiplication group $Mult(L)$ of a connected $2$-dimensional topological loop is a Lie group, then $Mult(L)$ is an elementary filiform nilpotent Lie group of dimension at least $4$. Moreover, we describe loops having…

Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…

We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In…

In light of $\phi$-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of…

Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages. The first one uses disjoint union on a suitable…

Each connected component of a mapping $\{1,2,...,n\}\rightarrow\{1,2,...,n\}$ contains a unique cycle. The largest such component can be studied probabilistically via either a delay differential equation or an inverse Laplace transform. The…

We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using…

We introduce a notion of finite approximate subloops in Moufang loops, with emphasis on the commutative case. For arbitrary Moufang loops we establish intrinsic product-set identities and covering consequences without passing through…

We study decomposable combinatorial labeled structures in the exp-log class, specifically, two examples of type a=1 and two examples of type a=1/2. Our approach is to establish how well existing theory matches experimental data. For…

Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus…

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by three involutions for $g\geq 6$.

In many quantum materials, strong electron correlations lead to the emergence of new states of matter. In particular, the study in the last decades of the complex phase diagram of high temperature superconducting cuprates highlighted…

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different closed surface. The second family of examples are defined on…

Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying the…

We study the magnetoconductance of electrons through a mesoscopic channel with antidots. Through quantum interference effects, the conductance maxima as functions of the magnetic field strength and the antidot radius (regulated by the…

In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We…