(The part of code is in Latex)
I was trying to visualise tensor product of two vector spaces $V$ and $W$ as $L$-Module ($L$ is Lie Algebra) under the operation $x.(v \otimes w)= x.v \otimes w + v \otimes x.w $ where $x \in L$, $v \in V$ and $w \in W$.
I want to verify the property:
$x.(as+bt)= a(x.s)+b(x.t)$ where $s$ and $t$ lie in $ V \otimes W$ and $a,b \in F$ where $F$ is field.[MATH][/MATH]
Please help in this regard.
I was trying to visualise tensor product of two vector spaces $V$ and $W$ as $L$-Module ($L$ is Lie Algebra) under the operation $x.(v \otimes w)= x.v \otimes w + v \otimes x.w $ where $x \in L$, $v \in V$ and $w \in W$.
I want to verify the property:
$x.(as+bt)= a(x.s)+b(x.t)$ where $s$ and $t$ lie in $ V \otimes W$ and $a,b \in F$ where $F$ is field.[MATH][/MATH]
Please help in this regard.