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We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudoreflection group $G$. When $G$ is a Coxeter group of simply-laced type we show$B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra ofsimply-laced type introduced by Cohen,Gijsbers and Wales[10]. We prove $B_G(\Upsilon)$ has a cellular structure and be semisimple for generic parameterswhen $G$ is a rank 2 Coxeter group. In the process of construction we introducea Cherednik type connection for BMW algebras and a generalization ofLawrence-Krammer representation to complex braid groups associated with allpseudo reflection groups.

Algebras associated with Pseudo Reflection Groups: A Generalization of Brauer Algebras