Abstract
A duality between the varieties of representations of ternary Lie algebras and superalgebras is established. The isomorphism of the lattices of subvarieties of ternary Lie algebras and superalgebras is induced by this duality. If a variety of (representations of) ternary Lie (super)algebras satisfies an identity of Young symmetry type D, then the dual variety satisfies an identity of Young symmetry type D*, and D is dual to D*. Finite basis systems of identities of ternary Lie algebras and superalgebras of infinite dimension as well as of representations of such algebras and superalgebras in their universal enveloping algebras are given in explicit form.
Published Version
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