Quantum homogeneous spaces and decomposable plane curves.
Angela Tabiri (University of Glasgow)
Wednesday 22nd November, 2017 15:00-16:00 Maths 311B
Abstract: Motivated by classical results for homogeneous spaces, for any plane curve of the form $f(y)=g(x)$, we construct the Hopf algebra $A(f,g)$ which is free over the coordinate ring $C$ of the curve with $C$ being a right coideal subalgebra of $A(f,g)$. This partly answers the conjecture that all plane curves are quantum homogeneous spaces. We use auxiliary Hopf algebras $A(x,a,g)$ and $A(y,a,f)$ to construct $A(f,g)$. Condition are given for when these Hopf algebras have properties such as being domains, noetherian, having finite Gelfand Kirillov dimension ...