Semidirect Products and Functional Equations for Quantum Multiplication
Abstract
The quantum integer [n]q is the polynomial 1 + q + q2 + ... + qn-1, and the sequence of polynomials [n]q n=1∞ is a solution of the functional equation fmn(q) = fm(q)fn(qm). In this paper, semidirect products of semigroups are used to produce families of functional equations that generalize the functional equation for quantum multiplication.
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