Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

Algebra seminar in Lincoln: talk by Isobel Webster

On the 25th of September 2019 Isobel Webster (University of Leeds) visited Charlotte Scott Centre for Algebra and gave a talk  “A lattice isomorphism theorem for cluster groups of type A”.

Abstract: Each quiver appearing in a seed of a skew-symmetric cluster algebra determines a corresponding group, which we call a cluster group, which is defined via a presentation. Grant and Marsh showed that, for quivers appearing in skew-symmetric cluster algebras of finite type, the associated cluster groups are isomorphic to finite reflection groups and thus are finite Coxeter groups. There are many well-established results for Coxeter presentations and it is natural to ask whether the cluster group presentations possess comparable properties.

I will define a cluster group associated to a cluster quiver and explain how the theory of cluster algebras forms the basis of research into cluster groups. As for Coxeter groups, we can consider parabolic subgroups of cluster groups. I will outline a proof which shows that, in the type A case, there exists an isomorphism between the lattice of subsets of the defining generators of the cluster group and the lattice of its parabolic subgroups.

 

One comment on “Algebra seminar in Lincoln: talk by Isobel Webster

  1. Evgeny Khukhro
    September 29, 2019

    Reblogged this on Maths & Physics News.

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Information

This entry was posted on September 29, 2019 by in research, Seminar, Visitors.

Blog Stats

  • 19,362 hits

Archives

%d bloggers like this: