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Irina Shchepochkina

Classification of the real simple Lie superalgebras of vector fields

Joint work with Dimitry Leites

We describe real simple Z-graded Lie superalgebras of vector fields with polynomial coefficients. Unlike the nonsuper case some simple complex Lie superalgebras of vector fields have more than one real form or have no real forms at all.

We show that the number of real forms also depends on the Z-grading: one can not consider real forms of just an abstract vectorial Lie superalgebra! One has to indicate a grading preserved.