Journal of Lie Theory 26 (2016), No. 4, 1145--1162
Copyright Heldermann Verlag 2016
A Class of Lie Conformal Superalgebras in Higher Dimensions
College of Science, Zhejiang Agriculture and Forestry University, Hangzhou 310027, P. R. China
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.
Keywords: Lie conformal superalgebra, Gel'fand-Dorfman bialgebra, Novikov-Poisson superalgebra, Novikov conformal superalgebra.
MSC: 17B60, 17B63, 17B67, 17B69, 17D99
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