  It is known that the recently discovered representations of the Artin groups
of type A_n, the braid groups, can be constructed via BMW algebras. We
introduce similar algebras of type D_n and E_n which also lead to the newly
found faithful representations of the Artin groups of the corresponding types.
We establish finite dimensionality of these algebras. Moreover, they have
ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with
respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the
corresponding Artin group generalizing the Lawrence-Krammer representation.
Finally we give conjectures on the structure, the dimension and parabolic
subalgebras of the BMW algebra, as well as on a generalization of deformations
to Brauer algebras for simply laced spherical type other than A_n.
