Averaging measured data is an important issue in computer vision and robotics. Integrating the pose of an object measured with multiple cameras into a single mean pose is one such example. In many applications data does not belong to a vector space. Instead, data often belongs to a non–linear group manifold as it is the case for orientation data and the group of three–dimensional rotations SO(3...

Neural computation in Clifford algebras, which include familiar complex numbers and quaternions as special cases, has recently become an active research field. As always, neurons are the atoms of computation. The paper provides a general notion for the Hessian matrix of Clifford neurons of an arbitrary algebra. This new result on the dynamics of Clifford neurons then allows the computation of o...

The topological nontriviality of insulating phases matter are by now well understood through K theory where the indices Dirac operators assembled into classes. We consider in context Kitaev chain a notion generalized operator associated Clifford algebra is centrally extended. demonstrate that central extension achieved via taking rational powers Pauli matrices appear corresponding BdG Hamiltoni...

In this paper, we study possible mathematical connections of the Clifford algebra with su(N)-Lie algebra, or in more physical terms links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin one-half fermion described by Dirac equation. The related matrix is worked out particular SU(2) outlined as well color gauge group SU(3). Possible perspectiv...

A straightforward two-line derivation of the Bekenstein-Hawking Area-Entropy relation in any dimension is shown based on Shannon’s information theory and Clifford algebras required by the New Relativity Principle. Recently we have proposed that a New Relativity principle may be operating in Nature which could reveal important clues to find the origins of M theory [1]. We were forced to introduc...

The Schur multiplier M(Ḡ1) ≅4 of the maximal subgroup Ḡ1 = 2⁶˙G₂(2)of Rudvalis sporadic simple group Ru is a cyclic order 4. Hence full representative R type 4.(2⁶˙G₂(2)) exists for Ḡ1. Furthermore, will have four sets IrrProj(Ḡ1;αi) irreducible projective characters, where associated factor α1, α2, α3 and α4, orders 1, 2, 4 4, respectively. In this paper, we deal with 2-fold cover 2. which can...

We study the notion of Γ-graded commutative algebra for an arbitrary abelian group Γ. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only simple finitedimensional associative graded commutative algebras over R or C. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras.

Clifford algebras are naturally associated with quadratic forms. These algebras are Z2 -graded by construction. However, only a Zn -gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V ) ↔ ∧ V and an ordering, guarantees a multivector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomor...

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued, rotation invariant, differential operator ∂ called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has ...