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Topological groups have representable internal actions
 
 
Description:  The actions of a group B on a group X correspond bijectively to the group homomorphisms from B to the group of automorphisms of X. This can be stated using representability of the functor 'actions on X' (see [2, 3]).

In this talk we show the corresponding result for topological groups: The continuous actions of a topological group B on a topological group X correspond bijectively to the continuous homomorphisms from B to the group of auto-homeomorphisms of X, equipped with a suitable topology. This result is based on previous joint work with F. Borceux and A. Montoli [1], where this result is proved for quasi-locally compact groups X, and a completely topological approach to the problem, obtained jointly with F. Cagliari [4].

 

[1] F. Borceux, M.M. Clementino, A. Montoli, On the representability of actions for topological algebras, Textos de Matemática, Série B, Vol. 46 (2014), pp. 41-66.

[2] F. Borceux, G.M. Kelly, G. Janelidze, On the representability of actions in a semi-abelian category, Theory Appl. Categ. 14 (2005), 85-104.

[3] F. Borceux, G.M. Kelly, G. Janelidze, Internal object actions, Comment. Math. Univ. Carolinae 46 82005), 235-255.

[4] F. Cagliari, M.M. Clementino, Topological groups have representable actions, in preparation.

Date:  2018-03-20
Start Time:   15:30
Speaker:  Maria Manuel Clementino (CMUC, Univ. Coimbra)
Institution:  CMUC
Place:  Room 5.5
Research Groups: -Algebra, Logic and Topology
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