Algebra Research Group

Welcome to the pages of the Algebra group in the Mathematical Institute at Oxford. Here you will find information on our members, the seminars and other events we organise, news about us and the research networks we participate in. There are also lists of lecture courses related to our interests.

The research interests of the group span group theory, representation theory and algebraic aspects of geometry, among many other topics. For more detailed information on the people in our group and their individual research interests, please see our list of members.

If you are interested in undertaking graduate studies with us, please see the department's information for prospective graduate students. Post-doctoral positions and funding opportunities and faculty positions are listed on the Institute's vacancies page.

Details of the next scheduled seminar in each of the series we organise are listed below. For future events, please follow the link to each seminar's listings.

Algebra seminar

22 May 2018
Anthony Joseph

Let $\mathfrak g$ be a semisimple Lie algebra.  A $\mathfrak g$-algebra is an associative algebra $R$ on which $\mathfrak g$ acts by derivations.  There are several significant examples.  Let $V$ a finite dimensional $\mathfrak g$ module and take  $R=\mathrm{End} V$ or $R=D(V)$ being the ring of derivations on  $V$ . Again take $R=U(\mathfrak g)$.   In all these cases  $ S=U(\mathfrak g)\otimes R$ is again a $\mathfrak g$-algebra.  Finally let $T$ denote the subalgebra of invariants of $S$.
For the first choice of $R$ above the representation theory of $T$ can be rather explicitly described in terms of Kazhdan-Lusztig polynomials.  In the second case the simple $T$ modules can be described in terms of the simple $D(V)$ modules.  In the third case it is shown that all simple $T$ modules are finite dimensional, despite the fact that $T$ is not a PI ring,  except for the case $\mathfrak  g =\mathfrak {sl}(2)$.

Representation Theory seminar

There are no seminars currently scheduled for this series.

An archive of previous events is also available.