Year: 2026
Type: article
Abstract: In this paper, we present the spinor structure associated with the Hyperbolic Clifford algebra of a real n-dimensional vector space V, which is denoted by ClHV. Unlike the standard Clifford algebra, the Hyperbolic Clifford algebra Cl(HV) simultaneously accommodates both multiforms and multivectors in a single algebraic structure, making it the natural framework—known as the “mother algebra”—for the study of superfields in theoretical physics and for generalizing the Clifford bundle formalism to hyperbolic structures arising in gravitational theories. The orthogonal groups and orthogonal transformations associated to the hyperbolic space HV are presented. The Clifford–Lipschitz group and the Pin and Spin groups associated with ClHV are defined. Then, the frame bundle and spinor structure associated to Hyperbolic Clifford algebra is derived.
Source: Axioms
Author: Eduardo Notte-Cuello
Institution: University of La Serena
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7154348536