Let g = g((0) over bar) circle plus g((1) over bar) be a finite-dimensional simple Lie superalgebra of type D(2, 1; alpha), G(3) or F(4) over C. Let G be the simply connected semisimple algebraic group over C such that Lie(G) = g((0) over bar) Suppose e is an element of g((0) over bar) is nilpotent. We describe the centralizer g(e) of e in ; and its center (ge) especially. We also determine the labeled Dynkin diagram for e. We prove theorems relating the dimension (z(g(e)))G(e) and the labeled Dynkin diagram.
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