nForum - Discussion Feed (Contraction as (co)derivation) 2021-10-19T17:44:48-04:00 https://nforum.ncatlab.org/ Lussumo Vanilla & Feed Publisher jim_stasheff comments on "Contraction as (co)derivation" (79969) https://nforum.ncatlab.org/discussion/10299/?Focus=79969#Comment_79969 2019-09-06T10:14:58-04:00 2021-10-19T17:44:48-04:00 jim_stasheff https://nforum.ncatlab.org/account/12/ The n-lab is very clear on contraction as a derivationFor example, there is a contraction of a vector $X\in V$ and a $n$-form $\omega\in \Lambda V^*$:$$(X,\omega)\mapsto \iota_X(\omega)$$and ... The n-lab is very clear on contraction as a derivation
For example, there is a contraction of a vector $X\in V$ and a $n$-form $\omega\in \Lambda V^*$:

$$(X,\omega)\mapsto \iota_X(\omega)$$

and $\iota_X: \omega\mapsto \iota_X(\omega)$ is a graded derivation of the exterior algebra of degree $-1$. This is also done for the tangent bundle which is a $C^\infty(M)$-module $V = T M$, then one gets the contraction of vector fields and differential forms. It can also be done in vector spaces, fibrewise.

Is it written somewhere about contraction of a $1$-form $\omega$ with an$n-vector$X\in \in \Lambda V\$ as a coderivation? ]]>