Related papers: On Clifford Algebras and binary integers

Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…

The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional…

This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)

A description of the real, complete modules over the Clifford algebra of a Hilbert space, with the elements of the latter acting by skew-symmetric operators.

In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

We calculate the degree of the algebra of covariants $\mathcal{C}_d$ for binary $d$-form. Also, for the degree we obtain its integral representation and asymptotic behavior.

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…

Gives an elementary exposition of the twisted group algebra rep- resentation of simple Clifford algebras

Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary…

We show that complex representations of Clifford algebra can always be reduced either to a real or to a quaternionic algebra depending on signature of complex space thus showing that complex spinors are unavoidably either real Majorana…

In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$.…

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…

Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford algebras in which the generators anticommute. In this paper,…

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…

We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…

We describe derivations of the Clifford algebra of a nondegenerate quadratic form on a countable dimensional vector space over an algebraically closed field of characteristic not equal to $2$. We also construct an algebraic automorphism of…