47. 2025.09.30 - Louis Rowen, Axial identities

Abstract

     48. 2025.10.14 - Sergey Shpectorov, Algebras of Monster type (2\eta,\eta) and the flip subalgebras

After reviewing double axes and the flip construction, we discuss the results of the joint project with Victor Bovdi classifying flips and flip subalgebras in the Matsuo algebras of extended symmetric groups. An important concept of an essential flip will be introduced, which helps to avoid repetitions among flip subalgebras and leads to more uniform properties of these subalgebras. Towards the end of the talk, we focus on the question under which conditions it can be shown that an algebra of Monster type (2\eta,\eta) can be obtained by the flip construction.

49. 2025.10.28 - Victor Petrov, Geometry of subalgebras in Brown algebra

Brown algebras are noncommutative algebras arising on the 56-dimensional representation of Lie algebras of type E7. Being noncommutative they still share common features with axial algebras. We study 32-dimensional subalgebras inside them and their possible mutual positions. This can be interpreted in terms of geometry of symmetric spaces of type EVI. The talk is based on a joint work with Andrei Semenov.

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Bibliography:

1) Axial algebras (non-official lecture notes), D. Craven, S. Shpectorov, 2017.

2) Axial algebras, J. McInroy, 2018 (update 2020).