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For the root system of type $A$ we introduce and study a certain extension ofthe quadratic algebra invented by S. Fomin and the first author, to construct amodel for the equivariant cohomology ring of the corresponding flag variety. Asan application of our construction we describe a generalization of theequivariant Pieri rule for double Schubert polynomials. For a general finiteCoxeter system we construct an extension of the correspondingNichols-Woronowicz algebra. In the case of finite crystallographic Coxetersystems we present a construction of extended Nichols-Woronowicz algebra modelfor the equivariant cohomology of the corresponding flag variety.

Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties