Bv-structure of the Cohomology of Nilpotent Subalgebras and the Geometry of (w-) Strings
نویسنده
چکیده
Given a simple, simply laced, complex Lie algebra g corresponding to the Lie group G, let n+ be the subalgebra generated by the positive roots. In this paper we construct a BV-algebra BV[g] whose underlying graded commutative algebra is given by the cohomology, with respect to n+, of the algebra of regular functions on G with values in ∧ (n+\g). We conjecture that BV[g] describes the algebra of all physical (i.e., BRST invariant) operators of the noncritical W [g] string. The conjecture is verified in the two explicitly known cases, g = sl2 (the Virasoro string) and g = sl3 (the W3 string). USC-95/32 ADP-95-59/M41 hep-th/9512032 December 1995
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