Its elements are formal sums with . In the direct
sum, only finitely many components of an element may be
nonzero. No analytic convergence is required for an element
of
(Chmutov and Duzhin 2005, p. 2).
Chmutov, S. and Duzhin, S. "The Kontsevich Integral." 15 Feb 2005. https://arxiv.org/abs/math/0501040v3.Chmutov,
S. and Duzhin, S. "Kontsevich Integral." In Encyclopedia of Mathematical
Physics, Vol. 3 (Ed. J.-P. Françoise, G. L. Naber,
and S. T. Tsou). Oxford, England: Elsevier, pp. 231-239, 2006. https://doi.org/10.1016/B0-12-512666-2/00241-8.
is the direct product
with 
. In the direct
sum 
, only finitely many components of an element may be
nonzero. No analytic convergence is required for an element
of 
(Chmutov and Duzhin 2005, p. 2).
is a nonnegatively graded algebra, its multiplication
extends to the graded completion by the rule
