Decomposable Curves which are Quantum Homogeneous Spaces

Let C be a decomposable plane curve over an algebraically closed field k of characteristic 0. That is, C is defined in k^2 by an equation of the form g(x) = f(y), where g and f are polynomials of degree at least 2. We use this data to construct 3 pointed Hopf algebras, A(x, a, g), A(y, b, f) and A(g, f), in the first two of which g [resp. f] are skew primitive central elements, and the third being a factor of the tensor product of the first two. We conjecture that A(g, f) contains the coordinate ring O(C) of C as a quantum homogeneous space, and prove this when each of g and f has degree at most 5 or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when g has degree 3, A(x, a, g) is a PBW deformation of the localisation at powers of a generator of the down-up algebra A(−1, −1, 0).

 

Online Zoom meeting (Session will open a few minutes before 16h)
https://videoconf-colibri.zoom.us/j/88286735278?pwd=aDVZaHdHbjY3THJ2RC84N20rRGhkZz09
Meeting ID: 882 8673 5278
Password: 319955

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

Angela Tabiri

Speaker's Institution

African Institute for Mathematical Sciences, Ghana

Area

Algebra and Geometry

Financiamento