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An analog of the classical invariant theory for Lie superalgebras. I, II. (English) Zbl 1002.17002
The author considers matrix Lie superalgebras and their invariants over the complex field. Assume \(V\) is a finite dimensional super space, and \(g\) a Lie superalgebra contained in \(gl(V)\). A collection of invariants is basic if these invariants together with their polarizations generate the algebra of invariants for the given Lie superalgebra.
The author describes basic sets of invariants for the following superalgebras: \(gl(V)\); \(sl(V)\); the orthosymplectic superalgebra \(osp(V)\); the peryplectic and the special peryplectic ones \(pe(V)\), \(spe(V)\), among others of the classical Lie superalgebras.

17A70 Superalgebras
15A72 Vector and tensor algebra, theory of invariants
17B70 Graded Lie (super)algebras
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