4 papers
A Poset Connected to Artin Monoids of Simply Laced Type
A. M. Cohen, D. A. H. Gijsbers, D. B. Wales
Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear…
BMW algebras of simply laced type
A. M. Cohen, D. A. H. Gijsbers, D. B. Wales
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 ty…
Linearity of Artin groups of finite type
Arjeh M. Cohen, David B. Wales
Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer's faithfulness proof for this linear…
Lie algebras generated by extremal elements
Arjeh M. Cohen, Anja Steinbach, Rosane Ushirobira +1
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra gener…