Related papers: Clifford Fibrations and Possible Kinematics

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is…

The geometry of nonholonomic bundle gerbes, provided with nonlinear connection structure, and nonholonomic gerbe modules is elaborated as the theory of Clifford modules on nonholonomic manifolds which positively fail to be spin. We explore…

In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.

Rotations in 3 dimensional space are equally described by the SU(2) and SO(3) groups. These isomorphic groups generate the same 3D kinematics using different algebraic structures of the unit quaternion. The Hopf Fibration is a projection…

A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…

A conic fibration has an associated sheaf of even Clifford algebras on the base. In this paper, we study the relation between the moduli spaces of modules over the sheaf of even Clifford algebras and the Prym variety associated to the conic…

The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of…

Prompted by a recent demonstration that the structure of a single quark-lepton generation may be understood via a Dirac-like linearization of the form p^2+x^2, we analyze the corresponding Clifford algebra in some detail. After classifying…

We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade…

The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…

This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor…

This paper is dedicated to the memory of Zbigniew Oziewicz, to his generosity, intelligence and intensity in the search that is science and mathematics. The paper begins with a basic construction that produces Clifford algebras inductively,…

In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Grassmann), multivectors and…

In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian…

We introduce a generalization, called a skew Clifford algebra, of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew…

We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is…

We gather conditions on a class H of continuous maps of topological spaces that allow a reasonable theory of fibrations up to an equivalence (a map from this class) which we call H-fibrations. The weak homotopy equivalences recover…

In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…

We introduce and study a new notion of stability for varieties fibered over curves, motivated by Koll\'ar's stability for homogeneous polynomials with integral coefficients. We develop tools to study geometric properties of stable…