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SUMMARY:Přemysl Jedlička (Czech University of Life Sciences\, Czechia)
DTSTART:20230403T150000Z
DTEND:20230403T160000Z
DTSTAMP:20260423T052502Z
UID:ENAAS/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/16/">N
 on-degenerate involutive set-theoretic solutions of the Yang-Baxter equati
 on of multipermutation level 2</a>\nby Přemysl Jedlička (Czech Universit
 y of Life Sciences\, Czechia) as part of European Non-Associative Algebra 
 Seminar\n\n\nAbstract\nSet-theoretic solution of the Yang-Baxter equation 
 is a mapping $r:X\\times X\\to X\\times X$ satisfying\n\\[ (r\\times 1) (1
 \\times r) (r\\times 1) = (1\\times r) (r\\times 1) (1\\times r). \\]\nA s
 olution $r: (x\,y)\\mapsto (\\sigma_x(y)\,\\tau_y(x))$ is called non-degen
 erate if the mappings $\\sigma_x$ and $\\tau_y$ are permutations\, for all
  $x\,y\\in X$. A solution is called involutive if $r^2=1$.\n\nIf $(X\,r)$ 
 is a non-degenerate involutive solution $(X\,r)$ then the relation~$\\sim$
  defined by $x\\sim y\\equiv \\sigma_x=\\sigma_y$ is a congruence. A solut
 ion is of multipermutation level 2 if $|(X/\\sim)/\\sim|=1$.\n\nIn our tal
 k we focus on these solutions and we present several constructions and pro
 perties.\n
LOCATION:https://researchseminars.org/talk/ENAAS/16/
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