BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:From Lie algebra crossed modules to tensor hierarchies\, and beyon
 d
DTSTART:20230616T120000Z
DTEND:20230616T130000Z
DTSTAMP:20260611T031300Z
UID:indico-event-9866@indico.math.cnrs.fr
DESCRIPTION:Speakers: Sylvain Lavau\n\nGauging procedures in supergravity 
 theories depart from classical gauge theories as in the former\, the gauge
  fields take values in the fundamental representation V of the Lie algebra
  g of global symmetries of the system. The consistency of the theory relie
 s on a pairing V-->g called the embedding tensor\, allowing to lift the Li
 e algebra structure of g to a Leibniz algebra structure on V. As is usuall
 y met in higher gauge theories\, if the gauge algebra is not Lie (here it 
 is Leibniz)\, it is replaced by some higher form of Lie algebras. Here\, s
 uch a higher structure is materialized by a differential graded Lie algebr
 a on a chain complex of g-modules\, called the tensor hierarchy. In the p
 resent talk we explain how tensor hierarchies are genetically related to L
 ie algebra crossed modules. Indeed\, two such algebras V and g\, together 
 with their embedding tensor\, form a triple called a Lie-Leibniz triple\, 
 of which Lie algebra crossed modules are particular cases. The canonical a
 ssignment (functor) associating to any Lie algebra crossed module its corr
 esponding unique 2-term differential graded Lie algebra can be extended to
  the category of Lie-Leibniz triples\, giving their associated tensor hier
 archies. This shows that Lie-Leibniz triples form natural generalizations 
 of Lie algebra crossed modules and that their associated tensor hierarchie
 s can be considered as some kind of 'lie-ization' of the former. Possible 
 applications of such a functor will be outlined.\n\nhttps://indico.math.cn
 rs.fr/event/9866/
LOCATION:Fokko du Cloux (Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/9866/
END:VEVENT
END:VCALENDAR