У оквиру семинара Групе за гравитацију, честице и поља Института за физику у Београду, у петак, 29. марта 2024. године у 11 часова, у сали 360 Института за физику у Београду, Петар Петрашиновић (Институт за физику у Београду) одржаће предавање:
2-groups and crossed modules: Classification and algorithm for constructing non-trivial ones
САЖЕТАК:
The 2-groups are category theory generalisations of the usual groups. They are equivalent to crossed modules, consisting of two groups, G and H, the homomorphism ∂ from H to G and the action ▷ from G
to H. One can construct a gauge theory of gravity on a 4-manifold based on crossed modules (like the BFCG theory for the Poincaré 2-group). Besides the usual group axioms, crossed modules must satisfy additional axioms. For this reason, they are much more rigid structures and more difficult to construct. There are some typical examples, but they are very rare and in which either ∂ or ▷ is trivial. In this seminar, I will discuss the properties of their linear structure-differential crossed modules. A possible way to classify these modules will be shown. Together with the classification, a corresponding algorithm for constructing differential cross modules with non-trivial ∂ and ▷ will be presented, which constructs them either for given groups G and H or for given ∂ and ▷.