BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marzia Mazzotta (University of Salento\, Italy) DTSTART:20230417T150000Z DTEND:20230417T160000Z DTSTAMP:20260423T035630Z UID:ENAAS/15 DESCRIPTION:Title: C lassification of set-theoretical solutions to the pentagon equation\nb y Marzia Mazzotta (University of Salento\, Italy) as part of European Non- Associative Algebra Seminar\n\n\nAbstract\nThe pentagon equation classical ly originates from the field of Mathematical Physics. Our attention is pla ced on the study of set-theoretical solutions of this equation\, namely\, maps $s: X \\times X \\to X \\times X$ given by $s(x\, y)=(xy\, \\theta_x( y))$\, where $X$ is a semigroup and $\\theta_x:X \\to X$ is a map satisfyi ng two laws. In this talk\, we give some recent descriptions of some clas ses of solutions achieved starting from particular semigroups. Into the sp ecific\, we provide a characterization of \\emph{idempotent-invariant} sol utions on a Clifford semigroup $X$\, that are those for which $\\theta_a$ remains invariant on the set of idempotents $E(X)$. In addition\, we will focus on the classes of \\emph{involutive} and \\emph{idempotent} solution s\, which are solutions fulfilling $s^2=id_{X \\times X}$ and $s^2=s$\, re spectively.\n LOCATION:https://researchseminars.org/talk/ENAAS/15/ END:VEVENT END:VCALENDAR