Let $F_m$ be the free metabelian Lie algebra of rank $m$ over a field $K$ characteristic 0. An automorphism $\varphi$ is called central if commutes with every inner $F_m$. Such automorphisms form centralizer $\text{\rm C}(\text{\rm Inn}(F_m))$ group Inn}(F_m)$ in Aut}(F_m)$. We provide an elementary proof to show that Inn}(F_m))=\text{\rm Inn}(F_m)$.

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold constructions associated the Niemeier lattice $V_N$ and certain 226 short automorphisms in $\operatorname{Aut}(V_N)$. show that up to algebraic conjugacy these are exactly generalised deep holes, introduced...

We construct a central extension of the group of automorphisms of a 2-Tate vector space viewed as a discrete 2-group. This is done using an action of this 2-group on a 2-gerbe of gerbel theories. This central extension is used to define central extensions of double loop groups.

We introduce a new approach to the representation theory of reductive p-adic groups G, based on the Geometric Invariant Theory (GIT) of Moy-Prasad quotients. Stable functionals on these quotients are used to give a new construction of supercuspidal representations of G having small positive depth, called epipelagic. With some restrictions on p, we classify the stable and semistable functionals ...

We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characte...