Related papers: Characterising Clifford parallelisms among Cliffor…

A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that…

We consider the Clifford algebra and the Clifford group associated with any quadratic module, degenerate or not, over an arbitrary commutative ring with 1. We determine some of the important subalgebras of the Clifford algebra under some…

The associative Cayley-Dickson algebras over the field of real numbers are also Clifford algebras. The alternative but nonassociative real Cayley-Dickson algebras, notably the octonions and split octonions, share with Clifford algebras an…

We consider Clifford algebras with nonsymmetric bilinear forms, which are isomorphic to the standard symmetric ones, but not equal. Observing, that the content of physical theories is dependent on the injection $\oplus^n\bigwedge…

We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…

The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more. Nevertheless, only sections of the hierarchy are fully…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

Albuquerque and Majid have shown how to view Clifford algebras $\cl_{p,q}$ as twisted group rings whereas Chernov has observed that Clifford algebras can be viewed as images of group algebras of certain 2-groups modulo an ideal generated by…

The paper is devoted to projective Clifford groups of quantum $N$-dimensional systems. Clearly, Clifford gates allow only the simplest quantum computations which can be simulated on a classical computer (Gottesmann-Knill theorem). However,…

This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply…

The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher…

Finite-dimensional representations of the proper orthochronous Lorentz group are studied in terms of spinor representations of the Clifford algebras. The Clifford algebras are understood as an `algebraic covering' of a full system of the…

We show that the automorphisms of the flag space associated with a 3-dimensional projective space can be characterized as bijections preserving a certain binary relation on the set of flags in both directions. From this we derive that there…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group -a property that is essential…

This article summarizes joint work with A. Alekseev (Geneva) on the Duflo isomorphism for quadratic Lie algebras. We describe a certain quantization map for Weil algebras, generalizing both the Duflo map and the quantization map for…

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…