# If a $k$-vector space $V$ is a simple $\mathfrak{sl}_2$-module then so is $V \otimes \bar{k}$?

Let $$V$$ be a finite dimensional $$k$$-vector space which is a simple $$\mathfrak{sl}_2$$-module. Here $$k$$ is a field of characteristic $$0$$ and we let $$\bar{k}$$ denote its algebraic closure.

I was wondering is $$V \otimes \bar{k}$$ still a simple $$\mathfrak{sl}_2$$-module? Any comments would be appreciated. Thank you.