IAM 02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Yang-Baxter operators in symmetric categories
Autor/es:
GUCCIONE, JUAN J.; VENDRAMIN, LEANDRO; GUCCIONE, JORGE A.
Revista:
COMMUNICATIONS IN ALGEBRA
Editorial:
TAYLOR & FRANCIS INC
Referencias:
Lugar: Londres; Año: 2018 vol. 46 p. 2811 - 2845
ISSN:
0092-7872
Resumen:
We introduce non-degenerate solutions of the Yang-Baxter equation in thesetting of symmetric monoidal categories. Our theory includes non-degenerateset-theoretical solutions as basic examples. However, infinite families ofnon-degenerate solutions (that are not of set-theoretical type) appear. As inthe classical theory of Etingof, Schedler and Soloviev, non-degeneratesolutions are classified in terms of invertible 1-cocycles. Braces and matchedpairs of cocommutative Hopf algebras (or braiding operators) are alsogeneralized to the context of symmetric monoidal categories and turn out to beequivalent to invertible 1-cocycles.
