Set-theoretic type solutions of the braid equation

Guccione J.A.; Guccione J.J.; Valqui C. · Journal of Algebra (2024) · DOI: 10.1016/j.jalgebra.2024.01.016

Resumen

In this paper we begin the study of set-theoretic type solution of the braid equation. Our theory includes set-theoretical solutions as basic examples. More precisely, the linear solution associated to a set-theoretic solution on a set X can be regarded as coming from the coalgebra kX, where k is a field and the elements of X are grouplike. We introduce and study a broader class of linear solutions associated in a similar way to more general coalgebras. We show that the relationships between set-theoretical solutions, q-cycle sets, q-braces, skew-braces, matched pairs of groups and invertible 1-cocycles remain valid in our setting.

Instituciones: Pontificia Universidad Católica del Perú