\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
Following the definition of a root basis of an affine root system, we define a base of the root system $R$ of an affine Lie superalgebra to be a linearly independent subset $B$ of the linear span of $R$ such that $B\sub R$ and each root can be written as a linear combination of elements of $B$ with integral coefficients such that all coefficients are non-negative or all coefficients are non-positive.
Characterization and classification of bases of root systems of affine Lie algebras are known in the literature; in fact, up to $\pm 1$-multiple, each base of an affine root system is conjugate with the standard base under the Weyl group action.
In the super case, the existence of those self-orthogonal roots which are not orthogonal to at least one other root, makes the situation more complicated. In this work, we give a complete characterization of bases of the root systems of twisted affine Lie superalgerbas. We precisely describe and classify them.
\end{document}