Diagonal mappings of set-theoretic solutions of the Yang-Baxter equation

Speaker(s)

Premysl Jedlicka

Affiliation

Czech University of Life Sciences Prague

Date

June 13, 2024, 12:15 p.m.

Information about the event

referat online

Title in Polish

Przekształcenia diagonalne teoriozbiorowych rozwiązań równania Yanga-Baxtera

Seminar

Seminar Algebra

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It is well known that, for involutive non-degenerate solutions of the Yang-Baxter equation, the operations $T(x)=\tau_x^{-1}(x)$ and $U(x)=\sigma_x^{-1}(x)$ are mutually inverse. We study these mappings in the non-involutive case, under different additional conditions (like bijectivity, non-degeneracy, left non-degeneracy). We also provide axiomatic description of multipermutation solutions which enables one to find a different shape of the diagonal mappings.

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