Interior product

In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, or inner derivation) is a degree −1 (anti)derivation on the exterior algebra of differential forms on a smooth manifold. The interior product, named in opposition to the exterior product, should not be confused with an inner product. The interior product ${\displaystyle \iota _{X}\omega }$ is sometimes written as ${\displaystyle X\mathbin {\lrcorner } \omega .}$^[1]