相关论文: Kinematic Mappings for Cayley-Klein Geometries via…

We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space…

Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry…

The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points,…

{\sc CLIFFORD} is a Maple package for computations in Clifford algebras $\cl (B)$ of an arbitrary symbolic or numeric bilinear form B. In particular, B may have a non-trivial antisymmetric part. It is well known that the symmetric part g of…

The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…

It is shown that classical Clifford algebras are group algebras of cyclic subgroups of arrowy rermutations. It is established that Euclidean 3-space, Pauli and Dirac algebras and groups of global guage transformations are corollary from the…

We provide explicit motion planners for Euiclidean configuration spaces. This allows us to recover some known values of the topological complexity and the Lusternik-Schinirelman category of these spaces.

We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…

This paper is the third of a series of three, and it is the continuation of math-ph/0412074 and math-ph/0412075. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint…

We introduce a spin field approach, that is compatible with the Cartan moving frame method, to describe the submanifold in a flat space. In fact, we consider a kind of spin field $\psi$, that satisfies a Killing spin field equation…

We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…

Let A be a cosemisimple Hopf *-algebra with antipode S and let $\Gamma$ be a left-covariant first order differential *-calculus over A such that $\Gamma$ is self-dual and invariant under the Hopf algebra automorphism S^2. A quantum Clifford…

I show how the isomorphism between the Lie groups of types $B_2$ and $C_2$ leads to a faithful action of the Clifford algebra $\mathcal C\ell(3,2)$ on the phase space of 2-dimensional dynamics, and hence to a mapping from Dirac spinors…

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flow on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits…

This paper explains how, following the representation of 3D crystallographic space groups in Clifford's geometric algebra, it is further possible to similarly represent the 162 so called subperiodic groups of crystallography in Clifford's…

This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adjoint and twisted adjoint representations. We prove that…

We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…