In mathematics, the cyclotomic identity states that
where M is Moreau's necklace-counting function,
and μ(·) is the classic Möbius function of number theory.
The name comes from the denominator, 1 − z j, which is the product of cyclotomic polynomials.
The left hand side of the cyclotomic identity is the generating function for the free associative algebra on α generators, and the right hand side is the generating function for the universal enveloping algebra of the free Lie algebra on α generators. The cyclotomic identity witnesses the fact that these two algebras are isomorphic.
There is also a symmetric generalization of the cyclotomic identity found by Strehl:
Famous quotes containing the word identity:
“Every man must define his identity against his mother. If he does not, he just falls back into her and is swallowed up.”
—Camille Paglia (b. 1947)