
Journal of Lie Theory 26 (2016), No. 4, 11451162 Copyright Heldermann Verlag 2016 A Class of Lie Conformal Superalgebras in Higher Dimensions Yanyong Hong College of Science, Zhejiang Agriculture and Forestry University, Hangzhou 310027, P. R. China hongyanyong2008@yahoo.com Fix a positive integer number r. A class of Lie conformal superalgebras in r dimensions called rdim ilinear Lie conformal superalgebras is studied for 1 ≤ i ≤ r. It is shown that an rdim ilinear Lie conformal superalgebra is equivalent to an (r1)dim super Gel'fandDorfman conformal bialgebra, which is a generalization of a superGel'fandDorfman bialgebra in the conformal sense. In particular, a special Lie conformal superalgebra named rdim linear Lie conformal superalgebra can be characterized by a generalized super Gel'fandDorfman 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. Keywords: Lie conformal superalgebra, Gel'fandDorfman bialgebra, NovikovPoisson superalgebra, Novikov conformal superalgebra. MSC: 17B60, 17B63, 17B67, 17B69, 17D99 [ Fulltextpdf (316 KB)] for subscribers only. 