Explicit Bracket in an Exceptional Simple Lie Superalgebra

This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3)∗, a subalgebra of vect(4|3). We derive differential equations for its elements, and solve these equations. Hence we get an exact form for the elements of cvect(0|3)∗. Moreover we realize cvect(0|3)∗ by ”glued” pairs of generating functions on a (3|3)-dimensional periplectic (odd symplectic) supermanifold and describe the bracket explicitly. 1991 Mathematics Subject Classification: 17A70.