Generalized Clifford Algebras and the N -th Root of Linear Differential Equations of Higher Order

Key Points

• This work aims to explore the application of generalized Clifford algebras in deriving the N-th root of higher-order linear differential equations.
• Constructed N-th order linear differential equations using generalized Clifford algebras.
• Applied factorization and cyclic permutation to convert higher-order equations into first-order equations.
• Investigated solutions related to the generalized Dirac equation and gauge theories.
• Explicit solutions to the N-th higher-order linear differential equations were determined.
• Connections between pseudo-unitary algebras, modular arithmetic, and ordinary Clifford algebras were noted.
• Discussion included relevance to modified Dirac equations and the Okubo algebra.