Primitive Homogeneous Spaces: We will give a brief description of homogeneous spaces of Lie groups, in particular an overview of how to analyze the geometric problem of classifying manifolds which admit a transitive action by some Lie group to the algebraic problem of classifying Lie subalgebras of its Lie algebra. Then we’ll apply the same method of thinking to the problem of primitive homogeneous spaces and give examples from the Lie group SL(2, R).

 

 

Partial Ordering in String Algebras: A quiver is a directed multi-graph with the possibility of self loops. Given a field, the algebra generated by the paths of a given quiver is said to be a path algebra. In particular, a string algebra is obtained by quotienting the path algebra by an ideal generated by a certain set of paths. In my talk, I will be giving a brief description of the conditions which characterise a string algebra. I will also discuss the definitions of strings and bands in a given string algebra and introduce a partial ordering amongst the strings which gives rise to hammocks in a given string algebra.