The noncritical 4D W_3 string is a model of W_3 gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the 2D (Virasoro) string. The physical operators form a BV-algebra. We model this BV-algebra on that of the polyderivations of a commutative ring on six variables with a quadratic constraint, or, equivalently, on the BV-algebra of (polynomial) polyvector fields on the base affine space of SL(3,C). Details have appeared elsewhere.
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