Related papers: Clifford theory for glider representations

We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…

Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups…

We solve the long standing problem of classification of standard compact Clifford-Klein forms of homogeneous spaces of simple non-compact real Lie groups under the extra assumption that $G$, $H$, $L$ are simple and absolutely simple. Then…

We translate the action of local Clifford operations on graph states into transformations on their associated graphs - i.e. we provide transformation rules, stated in purely graph theoretical terms, which completely characterize the…

Let A be a commutative ring with 1/2 in A. In this paper, we define new characteristic classes for finitely generated projective A-modules V provided with a non degenerate quadratic form. These classes belong to the usual K-theory of A.…

In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…

We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials,…

We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…

Let $\Gamma$ be a metric graph having a linear system $g^r_{2r}$ for some $2 \leq r \leq g-2$ then $\Gamma$ has a linear system $g^1_2$. This is similar to the well-known Clifford's Theorem from the theory of linear systems on smooth…

In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford…

In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Additionally, we provide an application to probability theory…

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

The Clifford defect is a rational number associated to the Weierstrass semigroup at a given point of an algebraic curve. It describes the error-correcting capability of the so-called Modified Algorithm for decoding the corresponding…

The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics. A few simple examples…

We list the subgroups of the basis set of Cl_{3,0} and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to +1 or -1, (2) the generators within the group anticommute, and…

This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of $\gamma^a$'s. Arranged into irreducible representations of…

We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an…

We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a…