Geodesic
A Class of Lie Conformal Superalgebras in Higher Dimensions
Journal of Lie theory, Tome 26 (2016) no. 4, pp. 1145-1162
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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.
Classification : 17B60, 17B63, 17B67, 17B69, 17D99
Mots-clés : Lie conformal superalgebra, Gel'fand-Dorfman bialgebra, Novikov-Poisson superalgebra, Novikov conformal superalgebra 
@article{JLT_2016_26_4_JLT_2016_26_4_a8,
     author = {Y. Hong},
     title = {A {Class} of {Lie} {Conformal} {Superalgebras} in {Higher} {Dimensions}},
     journal = {Journal of Lie theory},
     pages = {1145--1162},
     year = {2016},
     volume = {26},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a8/}
}
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Y. Hong. A Class of Lie Conformal Superalgebras in Higher Dimensions. Journal of Lie theory, Tome 26 (2016) no. 4, pp. 1145-1162. http://geodesic.mathdoc.fr/item/JLT_2016_26_4_JLT_2016_26_4_a8/