Skew braces and the YBE
March 22
Manoj Yadav
Automorphisms of extensions of skew braces and connections with cohomology
Abstract
Extensions of braces and skew braces have recently been developed and studied by many mathematicians, (co)homology theory has been introduced and extensions have been related to the second cohomology group (analogous to these concepts in group theory). C. Wells invented an exact sequence connecting automorphisms of group extensions with second cohomology group. Analogous study has been carried out for skew braces. In this talk I’ll speak on these aspects of skew braces.
Jonas Deré
Simply transitive NIL-affine actions of solvable Lie groups
Abstract:
Although not every 1-connected solvable Lie group G admits a simply transitive action via affine maps on R^n, it is known that such an action exists if one replaces R^n by a suitable nilpotent Lie group H, depending on G. However, not much is known about which pairs of Lie groups (G,H) admit such an action, where ideally you only need information about the Lie algebras corresponding to G and H. The most-studied case is when G is assumed to be nilpotent, then the existence of a simply transitive action is related to the notion of complete post-Lie algebra structures. In recent work with Marcos Origlia, we showed how this problem is related to the semisimple splitting of the Lie algebra corresponding to G. Our characterization not only allows us to check whether a given action is simply transitive, but also whether a simply transitive action exists given the Lie groups G and H. As a consequence, we show that every simply transitive action induces a post-Lie algebra structure, and characterize the ones in nilpotency class 2 coming from such an action by giving a new definition of completeness.