Abstract

We give a rigorous definition of Witten'sC*-string-algebra. To this end we present a new construction ofC*-algebras associated to special geometric situations (Kahler foliations) and generalize this later construction to the string case. Through this we get a natural geometrical interpretation of the string of semi-infinite forms as well as the fermionic algebra structure. Using the (non-commutative) geometric concepts for investigating the string algebra we get a natural Fredholm module representation of dimension 26+.

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