Rational representations of some algebraic varieties of -orthogonal groups.
We outline our recent results on bicovariant differential calculi on co-quasitriangular Hopf algebras, in particular that if is a quantum tangent space (quantum Lie algebra) for a CQT Hopf algebra A, then the space is a braided Lie algebra in the category of A-comodules. An important consequence of this is that the universal enveloping algebra is a bialgebra in the category of A-comodules.
Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group admits a special linear representation with non-amenable -Zariski closure if and only if it acts on an Abelian group (of...