Abstract
ABSTRACT Using translates, a characterization for the dual coalgebra of any Lie algebra is given. This characterization is analogous to the well known characterization for the dual coalgebra of any associative algebra. For any commutative, associative algebra and finite set of commuting derivations of satisfying a certain additional hypothesis, the structure of the dual coalgebra of the Lie subalgebra of is determined. This generalizes a result Nichols[1] proved for the case . As an application, the family of dual coalgebras which corresponds to the family of infinite-dimensional Lie algebras of derivations of polynomials in several indeterminates is then given.
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