Non-fixing graphs of skew braces

Speaker(s)

Arne Van Antwerpen

Affiliation

University of Ghent

Language of the talk

English

Date

Jan. 16, 2025, 12:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1

Information about the event

referat online

Seminar

Seminar Algebra

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In this talk, based on joint work with Silvia Properzi, we recall some core concepts of skew braces. Next, we introduce the non-fixing graph of a skew brace, inspired by the conjugacy class graph as defined by Bertram, Herzog and Mann. This graph measures the size of λ-orbits of a skew brace. We investigate some general properties of this graph and classify extremal cases. In particular, we classify the skew braces with a 1 vertex graph and those with a 2 vertex graph. If time allows, we discuss a straightforward extension of this graph and several other graphs related to set theoretic solutions and skew braces.

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