Related papers: Transgressive loop group extensions

We give a presentation of the universal central extension of the three-point loop algebra L over sl_2 by generators and relations. Our presentation arises from the realization of L as the tetrahedron Lie algebra and leads to connections…

Adjustments are additional structures on crossed modules of Lie groups, serving as a tool in higher gauge theory to circumvent the fake flatness of connections on 2-bundles. In this article, we investigate the existence and classification…

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the…

In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew…

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy…

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

We suggest an extension of a certain logarithm of the total Johnson map in terms of solvable Lie groups. Here, the domain of the map is extended to a subset consisting of exponential solvable elements in the mapping class group of a…

A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the…

The purpose of this paper is to investigate $(n+1)$-Lie algebras induced by $n$-Lie algebras and trace maps. We highlight a comparison of their structure properties (solvability, nilpotency) and the cohomology groups as well as central…

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…

We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are…

Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an…

The central extension of the Thompson group $T$ that arises in the quantized Teichm\"uller theory is 12 times the Euler class. This extension is obtained by taking a (partial) abelianization of the so-called braided Ptolemy-Thompson group…

Contents * Introduction -- Why $S^1$-extended phase space? -- Why central extensions of classical symmetries? * Central extension \Gt of a group $G$ -- Group cohomology -- Cohomology and contractions: Pseudo-cohomology -- Principal bundle…

In this review paper, we present several results on central extensions of the Lie algebra of symplectic (Hamiltonian) vector fields, and compare them to similar results for the Lie algebra of (exact) divergence free vector fields. In…

For a stratified group $G$, we construct a class of polarised Lie groups, which we call modifications of $G$, that are locally contactomorphic to it. Vice versa, we show that if a polarised group is locally contactomorphic to a stratified…

In this paper we study non-abelian extensions of a Lie group $G$ modeled on a locally convex space by a Lie group $N$. The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer…

We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families…

In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…

We study Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We collect general facts about them and discuss some examples arising in the study of restricted Lie algebras and quantum groups at roots of…