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:
“Personal change, growth, development, identity formation—these tasks that once were thought to belong to childhood and adolescence alone now are recognized as part of adult life as well. Gone is the belief that adulthood is, or ought to be, a time of internal peace and comfort, that growing pains belong only to the young; gone the belief that these are marker events—a job, a mate, a child—through which we will pass into a life of relative ease.”
—Lillian Breslow Rubin (20th century)