Stable isomorphisms for homology of algebras

Guy Boyde (Utrecht University)

Monday 6th November 16:00-17:00 Maths 311B


Homological stability is originally a property of (families of) groups, but recently, there has been a surge of interest in studying it for associative algebras too. Many results are now known (lots of them due to Rachael Boyd and Richard Hepworth).

Typically, the known results assert something stronger than stability, namely that

1) a certain family of group algebras includes into our family of algebras, and

2) this inclusion is a homology isomorphism in a range.

Stability then follows from stability for the groups, if known. I'll start with an overview of the area, and discuss how these "stable identifications" of the homology often hold in a range exceeding the stability range. The main examples will be the Partition and Jones annular algebras.

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