The Euler characteristic of an associative algebra


Venue   97th Peripatetic Seminar on Sheaves and Logic, Université Catholique de Louvain, Belgium, 31 January 2015.

Abstract   It was Steve Schanuel who established that the right way to "count" a topological space is to take its Euler characteristic -- that Euler characteristic is to spaces what cardinality is to sets. Pursuing his insight leads to a general definition of the Euler characteristic, or magnitude, of a (suitably finite) enriched category. Different choices of base category produce cardinality-like invariants in different branches of mathematics. I will describe what happens over Vect. In particular, every associative algebra A gives rise canonically to a certain Vect-enriched category, which in turn has an Euler characteristic; and as I will show, this is a recognizable homological invariant of A. This invariant perhaps deserves to be known as the Euler characteristic of an associative algebra.

Joint with Joe Chuang (City), Alastair King (Bath)

Slides   In this pdf file.

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