Related papers: Generalized triangle groups, expanders, and a prob…

It is known that a bi-orderable group has no generalized torsion element, but the converse does not hold in general. We conjecture that the converse holds for the fundamental groups of 3-manifolds, and verify the conjecture for…

One of the main open problems of mathematical physics is to consistently quantize Yang-Mills gauge theory. If such a consistent quantization were to exist, it is reasonable to expect a ``Wightman reconstruction theorem,'' by which a Hilbert…

We prove a graded version of Alev-Polo's rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras $A_n(k)$ cannot be isomorphic to their fixed subring under…

We construct new examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the families of finite subgroups, virtually abelian groups of bounded rank, and the family of virtually poly-cyclic subgroups. Our…

We introduce what we call `generalized higher rank $k$-graphs' as a class of categories equipped with a notion of size. They extend not only the higher rank $k$-graphs, but also the Levi categories introduced by the first author as a…

Let $G$ be a group. If an equation $x^n = y^n$ in $G$ implies $x = y$ for any elements $x$ and $y$, then $G$ is called an $R$--group. It is completely understood which knot groups are $R$--groups. Fay and Walls introduced $\bar{R}$--group…

We study 3-random-like graphs, that is, sequences of graphs in which the densities of triangles and anti-triangles converge to 1/8. Since the random graph ${\mathcal G}_{n,1/2}$ is, in particular, 3-random-like, this can be viewed as a weak…

We prove a generalisation of the Khukhro--Makarenko theorem on large characteristic subgroups with laws. This general fact implies new results on groups, algebras, and even graphs and other structures. Concerning groups, we obtain, e.g., a…

We study {\em generalized graph splines,} introduced by Gilbert, Viel, and the last author. For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type…

In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding…

In this paper, we study the category of trigroups as a generalization of the notion of digroup [4] and analyze their relationship with 3-racks [1] and Leibniz 3-algebras [6]. Trigroups are essentially associative trioids in which there are…

We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to…

We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…

Generalized Pascal matrix whose elements are generalized binomial coefficients is included in the group of generalized Riordan arrays. There is a special set of generalized Riordan arrays defined by parameter $q$. If $q=0$, they are…

We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…

We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The…

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless…

A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart…

We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured…

The constraints proposed recently by Bershadsky to produce $W^l_n$ algebras are a mixture of first and second class constraints and are degenerate. We show that they admit a first-class subsystem from which they can be recovered by…