A class of Lie conformal superalgebras in higher dimensions

Abstract

Fix a positive integer number $r$. A class of $r$-dim Lie conformal superalgebras named $r$-dim $i$-linear Lie conformal superalgebras are studied for $1\le i\le r$. We present an equivalent characterization of this class of Lie conformal superalgebras in $r$ dimension. Moreover, by this equivalent characterization, several constructions and examples are given.