G_a-actions of vertical type on affine T-varieties

We will discuss the paper due to A. Liendo. $\mathbb{G}_a$-actions of fiber type on affine $T$-varieties. J. Algebra 324 (2010), 3653-3665. We will talk about locally nilpotent derivations of vertical type and their classification for algebras $\mathcal{O}(X)$ for a normal affine $T$-variety $X$. Also we will discuss a general description for birational equivalence classes of affine varieties with Makar-Limanov invariant.