W Algebras, W Gravities and their Moduli Spaces

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By generalizing the Drinfel'd--Sokolov reduction we construct a large class of W algebras as reductions of Kac--Moody algebras. Furthermore we construct actions, invariant under local left and right W transformations, which are the classical covariant induced actions for W gravity. Talk presented by T. Tjin at the Trieste Summerschool on strings and related topics.
8 pages, THU-92/26, ITFA-92/24

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