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:
“Let it be an alliance of two large, formidable natures, mutually beheld, mutually feared, before yet they recognize the deep identity which beneath these disparities unites them.”
—Ralph Waldo Emerson (1803–1882)