BMW algebras of simply laced type

Abstract 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 ⊂ 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 .