This is an announcement for the paper "Noncommutative Riesz transforms I-an algebraic approach" by Marius Junge. Abstract: Riesz transforms on Rn or Riemanian manifolds are classical examples of singular integrals. In this paper we consider Riesz transforms associated to a semigroup Tt of completely positive trace preserving maps on a finite von Neumann algebra. Given a generator A of the semigroup we consider the square of the gradient Gamma(x,y)=A(x^*y)-A(x^*)y-x^*A(y) We prove un upper bound ||\Gamma(x,x)^{1/2}\|_p \le c(p) || (-\Delta)^{1/2}x ||_p under suitable assumptions. These estimates generalizes commutative results by P.A. Meyer, Bakry, Emry, Gundy, Piser. Key tools are square function inequalities obtained in joint work with C. Le Merdy and Q. Xu and new algebraic relations. As an application we obtain new examples of quantum metric spaces for discrete groups with the Haagerup property and rapid decay. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L25 The source file(s), mainfile2.tex: 192365 bytes, is(are) stored in gzipped form as 0801.1873.gz with size 59kb. The corresponding postcript file has gzipped size 283kb. Submitted from: junge@math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.1873 or http://arXiv.org/abs/0801.1873 or by email in unzipped form by transmitting an empty message with subject line uget 0801.1873 or in gzipped form by using subject line get 0801.1873 to: math@arXiv.org.