The classification of 3-transposition groups has a long history. In particular, it is a highly non-trivial fact that finitely generated 3-transposition groups are finite. We provide an alternative viewpoint on this question using the corresponding ‘Matsuo algebras’, a class of non-associative algebras. These are instances of primitive axial algebras of Jordan type. We prove that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional (and this bound is sharp).
This is joint work with Louis Rowen and Yoav Segev (to appear in Proc. AMS).
This video is part of the Non-Associative Day in Online, run by the European Non-Associative Algebra Seminar series.
