For a connected $n$-manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a point $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\}$. Of course $L_{p}$ is a Lie subalgebra of $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension-$n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to) $L_{p}$ for some $p\in M$?

Here is a related post.

For a connected $n$-manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a point $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\}$. Of course $L_{p}$ is a Lie subalgebra of $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension-$n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to) $L_{p}$ for some $p\in M$?

Here is a related post.

For a connected $n$ manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a pointe $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\} $.Of course $L_{p}$ is a Lie subalgebra of  $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension $n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to)  $L_{p}$ for some $p\in M?$

Here is a related post:

The minimum codimension of Lie subalgebra of $\chi^{\infty}(M)$

For a connected $n$-manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a point $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\}$. Of course $L_{p}$ is a Lie subalgebra of $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension-$n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to) $L_{p}$ for some $p\in M$?

Here is a related post.

For a connected $n$ manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a pointe $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\} $.Of course $L_{p}$ is a Lie subalgebra of $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension $n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to) $L_{p}$ for some $p\in M?$

For a connected $n$ manifold $M$, the Lie algebra of all smooth vector fields is denoted by $\chi^{\infty}(M)$. For a pointe $p\in M$ we define $L_{p}=\{X\in \chi^{\infty}(M)\mid X(p)=0\} $.Of course $L_{p}$ is a Lie subalgebra of $\chi^{\infty}(M)$ whose codimension is equal to $n$.

Is it true that every codimension $n$ Lie subalgebra of $\chi^{\infty}(M)$ is necessarily in the form of (or isomorphic to) $L_{p}$ for some $p\in M?$

Here is a related post:

The minimum codimension of Lie subalgebra of $\chi^{\infty}(M)$