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SUMMARY:Manuel Mancini (University of Palermo\, Italy)
DTSTART:20250120T150000Z
DTEND:20250120T160000Z
DTSTAMP:20260423T021146Z
UID:ENAAS/107
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/107/">
 On the representability of actions of non-associative algebras</a>\nby Man
 uel Mancini (University of Palermo\, Italy) as part of European Non-Associ
 ative Algebra Seminar\n\n\nAbstract\nIt is well known that in the semi-abe
 lian category Grp of groups\, split extensions\, or equivalently internal 
 actions\, are represented by automorphisms. This means that the category G
 rp is action representable and the actor of a group X is the group Aut(X).
  The notion of action representable category has proven to be quite restri
 ctive: for instance\, if a non-abelian variety of non-associative algebras
 \, over an infinite field of characteristic different from two\, is action
  representable\, then it is the category of Lie algebras. More recently G.
  Janelidze introduced the notion of weakly action representable category\,
  which includes a wider class of categories. In this talk we show that for
  an algebraically coherent variety of algebras and an object X of it\, it 
 is always possible to construct a partial algebra E(X)\, called external w
 eak actor of X\, which allows us to describe internal actions on X. Moreov
 er\, we show that the existence of a weak representation is connected to t
 he amalgamation property\, and we give an application of the construction 
 of the external weak actor in the context of varieties of unitary algebras
 . This is joint work with J. Brox\, (Universidad de Valladolid)\, Xabier G
 arcía Martínez (Universidade de Vigo)\, Tim Van der Linden and Corentin 
 Vienne (Université catholique de Louvain).\n
LOCATION:https://researchseminars.org/talk/ENAAS/107/
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