The Family of Khodakovsky Superalgebras X_q: Definitions, Structure, Spectral Decomposition, and Categorical Duality

In a series of works [1-6] an algebraic construction was developed that describes the dynamical change of the dimension of configuration space. In the present work these constructions are systematized in the form of a unified family of Khodakovsky superalgebras X_q, where the parameter q = 0,1,2,3,4,5 corresponds to the successive extension of the original algebra X (dimension n, rank m) through the introduction of negative indices, annihilators, a Z2-grading, a dynamical type, and, finally, a f