Related papers: Poincar\'e theory for compact abelian one-dimensio…
For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…
A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the…
This paper considers a generalisation of the idea of a Hopf algebra in which a commutative ring replaces the field in the unit and counit. It is motivated by an example from the inverse scattering formalism for solitons. We begin with the…
The Poincar\'e-Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of $C^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly…
The fibre bundle construct defined in our previous work continues to be the context for this paper; quantum fields composed of fibre algebras become liftings of; or sections through; a fibre bundle with base space a subset of curved…
It is well-known that the Eulerian polynomials, which count permutations in $S_n$ by their number of descents, give the $h$-polynomial/$h$-vector of the simple polytopes known as permutohedra, the convex hull of the $S_n$-orbit for a…
Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is…
This paper presents a study of the Poincar\'e-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant…
Fourier coefficients of automorphic representations $\pi$ of $\Sp_{2n}(\BA)$ are attached to unipotent adjoint orbits in $\Sp_{2n}(F)$, where $F$ is a number field and $\BA$ is the ring of adeles of $F$. We prove that for a given $\pi$, all…
To study singularities on complex varieties we study Poincar\'e series of filtrations that are defined by discrete valuations on the local ring at the singularity. In all previous papers on this topic one poses restrictions on the centers…
This paper studies homeomorphisms of the closed annulus that are isotopic to the identity from the viewpoint of rotation theory, using a newly developed forcing theory for surface homeomorphisms. Our first result is a solution to the so…
We discover a new Poincar\'e type phenomenon by establishing an optimal rigidity theorem for local CR mappings between circle bundles that are defined in a canonical way over (possibly reducible) bounded symmetric domains. We prove such a…
We compute the total cohomology of the complement of the toric arrangement associated to the root system $A_n$ as a representation of the corresponding Weyl group via fixed point theory of a "twisted" action of the group. We also provide…
The primary purpose of this paper concerns the relation of (compact) generalized manifolds to finite Poincar\'{e} duality complexes (PD complexes). The problem is that an arbitrary generalized manifold $X$ is always an ENR space, but it is…
We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Cech cohomology group of the closure of the image of the map. We show that this group generalizes…
The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…
This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…