BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Almost involutive Hopf algebras: are there additional symmetries i
n Hopf algebras besides the antipode?
DTSTART;VALUE=DATE-TIME:20140625T070000Z
DTEND;VALUE=DATE-TIME:20140625T080000Z
DTSTAMP;VALUE=DATE-TIME:20200716T175150Z
UID:indico-contribution-586@indico.math.cnrs.fr
DESCRIPTION:Speakers: Walter Ferrer-Santos (Universidad de la Republica\,
Montevideo)\nAn involutory Hopf algebra is a Hopf algebra whose antipode s
quared equals the identity\, $S^2=\\operatorname{id}$. \n\nThe identity ma
p is an automorphism of Hopf algebras\, hence it is tempting to substitute
$\\operatorname{id} \\mapsto \\sigma$ where $\\sigma$ is an arbitray Hopf
morphism and consider Hopf algebras whose antipode (that is an antimorphi
sm of Hopf algebras) squared is the square of a Hopf automorphism\, $\\ant
^2=\\sigma^2$. A map such as $\\sigma$ if it exists\, is called a companio
n morphism. \n\nIf $\\ant$ has finite order\, so does $\\sigma$. A morphis
m of a given mathematical structure that is of finite order may be interpr
eted as a symmetry of the structure.\n\nHence\, the companion morphism ca
n be interpreted as an additional symmetry of the structure of $H$. If the
Hopf algebra $H$ admits a companion morphism\, we say that it is almost i
nvolutory (AI). \n\nThe purpose of this talk\, is to define and consider t
he initial properties of almost involutory Hopf algebras. We prove that up
to dimension 15 all Hopf algebras except a few types in dimensions eight
and twelve are AI.\n\nhttps://indico.math.cnrs.fr/event/158/contributions/
586/
LOCATION:UniversitÃ© Lille 1 Salle de rÃ©unions
URL:https://indico.math.cnrs.fr/event/158/contributions/586/
END:VEVENT
END:VCALENDAR