Comments on non-commuting variables, n-ary algebras, and first-order differential equations

Abstract

Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic systems based on non-associative algebras are presented. A system related to a Li\'enard system associated to an Abel's differential equation of the second kind is given as an example.