REVOLUTIONIZING MATRIX ISOMORPHISMS OF COMPLEX CLIFFORD ALGEBRAS THROUGH CANTOR SET

Abstract

The study of complex Clifford algebras and their representations plays a significant role in determining the geometric and topological structures of manifolds. This article presents a novel approach for obtaining the standard isomorphisms of complex Clifford algebras using the Cantor set. Specifically, the article constructs a representation for even complex Clifford algebra Cl2n using a specific 2n-element subset derived from the Cantor set, where Vn denotes the set of left endpoints. By constructing an algebra homomorphism from Cl2n to B(Fn) and a base for the representation space Fn, the matrix of any Clifford generator's image under this representation is found to emerge as the tensor product of standard Pauli matrices. Additionally, the article introduces tilt and switch operators on Fn, similar to those used to represent infinite dimensional complex Clifford algebra, for construction purposes. Overall, this new method provides a useful tool for further exploration and understanding of complex Clifford algebras