Using the formalism of noncommutative symmetric functions, we derive the basic theory of the peak algebra of symmetric groups and of its graded Hopf dual. Our main result is to provide a representation theoretical interpretation of the peak algebra and its graded dual as Grothendieck rings of the tower of Hecke–Clifford algebras at q 1⁄4 0: r 2004 Elsevier Inc. All rights reserved.

In this paper we study in details the properties of the duality product of multivectors and multiforms (used in the definition of the hyperbolic Clifford algebra of multivefors) and introduce the theory of the k multivector and l multiform variables multivector (or multiform) extensors over V (defining the spaces ext l k (V ) and ∗ ext l k (V )) studying their properties with considerable detail.

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 1. A Clifford algebra criterion for (ν,Bg) to be of Lie type . . . . . . . . . . . . . . . . . . 455 2. The cubic Dirac operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 3. Tensoring with the spin representat...

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 link between the two approaches. Finally, we give some notions of the generalisations to arbitrary spacetimes, by the introduction of the spin and spinor bundles.

A special approach to the geometrization the theory of the electron has been proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. New experiments concerning the geometric nature wave function...

A model of Emergent Gravity with the observed Cosmological Constant from a BF-Chern-Simons-Higgs Model is revisited which allows to show how a Conformal Gravity, Maxwell and SU(2) × SU(2) × U(1) × U(1) Yang-Mills Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in a very natural and geometric fashion.

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors an...