Simple groups of Lie type and linear algebraic groups have a long history and play an important role in mathematics. Mathematicians classify them by their Dynkin diagrams into simply laced types and non-simply laced types. But these two kinds are not isolated from each other. It is a very classical knowledge that simple groups of Lie types of non-simply laced type can be attained from the simply laced ones by considering nontrivial automorphisms of their Dynkin diagrams. This idea was extended to a more general theory called admissible partition by M¨uhlherr in the 1990s. In this thesis, we apply these ideas to the Brauer algebras of simply-laced type which are studied by Cohen, Frenk and Wales and de¿ne Brauer algebras of non-simply laced type by generators and relations. We prove that they are free, compute their ranks and ¿nd bases by use of combinatorial data on their root systems; we also prove their cellularity in the sense of Graham and Lehrer. (Conclusions are shown in table, but not visible in this abstract) In this thesis, we use many results of Brauer algebras of simply laced type, such as their normal forms, their representations on collections of special mutually orthogonal root sets, and their diagram representations. Also we use a lot of algebraic computations to ¿nd normal forms for monomials in the algebras of non-simply laced type.
|Kwalificatie||Doctor in de Filosofie|
|Datum van toekenning||6 jun 2012|
|Plaats van publicatie||Eindhoven|
|Status||Gepubliceerd - 2012|