In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems ...

A bivariate representation of a complex simple Lie algebra is an irreducible representation whose highest weight is given by a combination of the first two fundamental weights. For a complex classical Lie algebra, we ...

We explore a method for explicitly constructing multiplicative 2-cocycles for bosonizations of Nichols algebras B(V ) over Hopf algebras H. These cocycles arise as liftings of H-invariant linear functionals on V⊗ V and ...

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case ...