In this paper, we give a characterization of the quasi-linear left cycle sets A with Rad(A) Soc(A) via unitary metahomomorphisms and a complete description of those with Rad(A) Fix(A) = Soc(A) improving the results obtained in [F. Catino and M. M. Miccoli, Construction of quasi-linear left cycle sets, J. Algebra Appl. 14(1) (2015), Article ID:1550001, 1-7]. Moreover, we develop a theory of dynamical extensions of quasi-linear left cycle sets to provide new set-theoretic solutions of the Yang-Baxter equation that are non-degenerate, involutive and multipermutational.
Dynamical extensions of quasi-linear left cycle sets and the Yang-Baxter equation
Castelli M.;Catino F.;Miccoli M. M.;Pinto G.
2019-01-01
Abstract
In this paper, we give a characterization of the quasi-linear left cycle sets A with Rad(A) Soc(A) via unitary metahomomorphisms and a complete description of those with Rad(A) Fix(A) = Soc(A) improving the results obtained in [F. Catino and M. M. Miccoli, Construction of quasi-linear left cycle sets, J. Algebra Appl. 14(1) (2015), Article ID:1550001, 1-7]. Moreover, we develop a theory of dynamical extensions of quasi-linear left cycle sets to provide new set-theoretic solutions of the Yang-Baxter equation that are non-degenerate, involutive and multipermutational.File in questo prodotto:
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