Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493517 | Journal of Algebra | 2005 | 47 Pages |
Abstract
It is known that the recently discovered representations of the Artin groups of type An, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type Dn and En 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 I1 and I2 with I2âI1 such that the quotient with respect to I1 is the Hecke algebra and I1/I2 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 An.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Arjeh M. Cohen, Dié A.H. Gijsbers, David B. Wales,