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{\bf M. Farrokhi D. G.}
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{\bf An Identity Generator: Basic Commutators}
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We introduce a group theoretical tool on which one can derive a
family of identities from sequences that are defined by a recursive
relation. As an illustration it is shown that
$$\sum_{i=1}^{n-1}F_{n-i}F_i^2
={1\over2}\sum_{i=1}^n(-1)^{n-i}(F_{2i}-F_i)
={F_{n+1}\choose2}-{F_n\choose2},
$$
where $\{F_n\}$ denotes the sequence of Fibonacci numbers.



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