The hamiltonian quantum dynamical structures in the Gel’fand triplets of spaces used in preceding installments to describe correlated hamiltonian dynamics on phase space by quasi-invariant measures are shown to possess a covering structure, which is constructed explicitly using the properties of Clifford algebras. The unitary Clifford algebra is constructed from the intersection of the orthogon...

Conventional formulations of linear algebra do not do justice to the fundamental concepts of meet, join, and duality in projective geometry. This defect is corrected by introducing Clifford algebra into the foundations of linear algebra. There is a natural extension of linear transformations on a vector space to the associated Clifford algebra with a simple projective interpretation. This opens...

1. Historical Developments About 150 years ago, in 1844, the German high school teacher Hermann Grassmann published an ambitious work entitled The Linear Extension Theory, A New Branch of Mathematics. For Grassmann this was indeed The Branch of mathematics, which in his own words “far surpasses” all others. His subsequent work Geometric Algebra won the prize of 45 gold ducats set out by the Pri...

A set of valuable universal similarity factorization equalities are established over complex Clifford algebras Cn. Through them matrix representations of complex Clifford algebras Cn can directly be derived, and their properties can easily be determined. AMS Subject Classification: 15A23, 15A66.

This paper is concerned with the modular representation theory of the affine Hecke-Clifford superalgebra, the cyclotomic Hecke-Clifford superalgebras, and projective representations of the symmetric group. Our approach exploits crystal graphs of affine Kac-Moody algebras.

We describe the canonical model of an algebraic curve of genus 9 over a perfect field when the Clifford index is maximal (=3) by means of linear systems of higher rank. Let SpG(n, 2n) be the symplectic Grassmannian, that is, the Grassmannian of Lagrangian subspaces of a 2n-dimensional symplectic vector space, over a field k. In the case n = 3, SpG(3, 6) is a 6-dimensional homogeneous variety an...

Abstract The paper is devoted to the generalization of Vinberg theory homogeneous convex cones. Such a cone described as set “positive definite matrices” in commutative algebra ? n Hermitian T-matrices. These algebras are Euclidean Jordan and consist × matrices A = ( ij ), where ii ? ?, entry for i < j belongs some vector space V ; ????) $$ {a}_{ji}={a}_{ij}^{\ast }=\mathfrak{g}\left({a}_{ij...

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles ( bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D4−D5−E6−E7−E8 model of Smith based on the underlying Clifford algebraic structures in D = 8...

The first comprehensive revision of the Western Palaearctic species of the genus Dinotrema Foerster, 1862 is provided. 174 species of this genus are redescribed and illustrated. Ten species are described as new, viz, D. acompressum sp. nov., D. cahitum sp. nov., D. collybiae sp. nov., D. digitatum sp. nov., D. glabrideum sp. nov., D. helote sp. nov., D. lepiotae sp. nov., D. norwegicum sp. nov....