Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation
AbstractUsing the theory of cycle sets and braces, non-degenerate indecomposable involutive set-theoretic solutions to the Yang–Baxter equation are classified in terms of their universal coverings and their fundamental group. The universal coverings are characterized as braces with an adjoint orbit generating the additive group. Using this description, all coverings of non-degenerate indecomposable cycle sets are classified. The method is illustrated by examples.
2017 ◽
Vol 147
(6)
◽
pp. 1279-1295
2005 ◽
Vol 14
(02)
◽
pp. 189-215
◽
Keyword(s):
2018 ◽
Vol 11
(06)
◽
pp. 1850082
Keyword(s):
1998 ◽
Vol 58
(2)
◽
pp. 233-237
Keyword(s):
2014 ◽
Vol 14
(01)
◽
pp. 1550001
◽