Related papers: Spinorial discrete symmetries and adjoint structur…
This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost…
There are many results showing the connection and phenomenon between some low-dimensional manifolds with the profinite completions of their fundamental groups. We focus on some Seifert 4-manifolds about the extent of their profinite…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…
In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and…
We present a theory and applications of discrete exterior calculus on simplicial complexes of arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory includes not only discrete differential forms but…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special K\"ahler holonomy. Motivated by certain curvature…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…
For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We walk out the landscape of K-theoretic Poincare Duality for finite algebras. It paves the way to get continuum Dirac operators from discrete noncommutative manifolds.
In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial…