Semidirect Products and Functional Equations for Quantum Multiplication

Details Semidirect Products and Functional Equations for Quantum Multiplication Semidirect Products and Functional Equations for Quantum Multiplication

2006-11-20

arxiv.org/abs/math/0611619v1

Mathematics

Number Theory

7 pages

Scientific paper

The quantum integer [n]_q is the polynomial 1 + q + q^2 + ... + q^{n-1}, and
the sequence of polynomials { [n]_q }_{n=1}^{\infty} is a solution of the
functional equation f_{mn}(q) = f_m(q)f_n(q^m). 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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