We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; and La, V. Kato, "Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras" (2016). CUNY Academic Works.