  The open string field theory of Witten (SFT) has a close formal similarity
with Chern-Simons theory in three dimensions. This similarity is due to the
fact that the former theory has concepts corresponding to forms, exterior
derivative, wedge product and integration over the manifold. In this paper, we
introduce the interior product and the Lie derivative in the $KBc$ subsector of
SFT. The interior product in SFT is specified by a two-component "tangent
vector" and lowers the ghost number by one (like the ordinary interior product
maps a $p$-form to $(p-1)$-form). The Lie derivative in SFT is defined as the
anti-commutator of the interior product and the BRST operator. The important
property of these two operations is that they respect the $KBc$ algebra.
Deforming the original $(K,B,c)$ by using the Lie derivative, we can consider
an infinite copies of the $KBc$ algebra, which we call the $KBc$ manifold. As
an application, we construct the Wilson line on the manifold, which could play
a role in reproducing degenerate fluctuation modes around a multi-brane
solution.
