Algebraic and Geometric Structures in String Backgrounds

We give a brief introduction to the study of the algebraic structures – and their geometrical interpretations – which arise in the BRST construction of a conformal string background. Starting from the chiral algebra A of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson structure, known as a Gerstenhaber algebra, on the BRST cohomology of A . For the 2D string background, the correponding G-algebra can be partially described in term of a geometrical G-algebra of the affine plane C . This paper will appear in the proceedings of Strings 95.