Journal of Lie Theory

Fix a positive integer number r. A class of Lie conformal superalgebras in r dimensions called r-dim i-linear Lie conformal superalgebras is studied for 1 ≤ i ≤ r. It is shown that an r-dim i-linear Lie conformal superalgebra is equivalent to an (r-1)-dim super Gel'fand-Dorfman conformal bialgebra, which is a generalization of a super-Gel'fand-Dorfman bialgebra in the conformal sense. In particular, a special Lie conformal superalgebra named r-dim linear Lie conformal superalgebra can be characterized by a generalized super Gel'fand-Dorfman algebra which has a Lie superalgebra structure and r Novikov superalgebra structures adjoint with some compatibility conditions. Moreover, by these equivalent characterizations, several constructions and examples of Lie conformal superalgebras in higher dimensions are given.