Related papers: Extensions of Current Groups on S^3 and the Adjoin…

We prove that the automorphism group of a compact 6-manifold $M$ endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min$\{5,b_1(M)\}$. Moreover, we study the properties of the automorphism…

We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi…

In this paper we show how to obtain the heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the $\mathrm{SL}(5)$ exceptional field theory and show that when the extended space…

We consider a U(1) x SU(2) gauge theory on the four-dimensional manifold S^1 x S^3. If we make the assumption that only gauge transformations connected to the identity are allowed, the winding numbers of U(1) around S^1 and of SU(2) around…

We analyze the group structures of two groups of order 1344 which are respectively non-split and split extensions of the elementary Abelian group of order 8 by its automorphism group PSL_2(7).They share the same character table. The group…

We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness…

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its…

The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of \'etale Lie 2-groups. In finite dimensions, central extensions of Lie algebras integrate to…

A special symplectic Lie group is a triple $(G,\omega,\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure…

We modify Ginzburg's construction for the Adjoint L function of GL(3) (unfolding and unramified computations only) to accomodate quasisplit unitary groups.

In this paper, we first give the notation of a compatible pre-Lie algebra and its representation. We study the relation between compatible Lie algebras and compatible pre-Lie algebras. We also construct a new bidifferential graded Lie…

A composite non-abelian model $SU(N) \times SU(N)$ is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by $SU(N) \times SU(N)$. The…

We discuss the nonlinear extension of $N=2$ superconformal algebra by generalizing Sugawara construction and coset construction built from $N=2$ currents based on Kazama-Suzuki $N=2$ coset model $\frac{SU(3)}{SU(2) \times U(1)}$ in $N=2$…

We classify the possible finite symmetries of conformal field theories with an affine Lie algebra su(2) and su(3), and discuss the results from the perspective of the graphs associated with the modular invariants. The highlights of the…

There are three main components to this article: (i) A formula for the eta invariant of the signature complex for any finite subgroup of ${\rm{SO}}(4)$ acting freely on $S^3$ is given. An application of this is a non-existence result for…

It was recently demonstrated that the N=0,1,2,4 super-Schwarzian derivatives can be constructed by applying the method of nonlinear realizations to the finite-dimensional (super)conformal groups SL(2,R), OSp(1|2), SU(1,1|1), and SU(1,1|2),…

The present paper starts with an introduction to quaternions and then defines the 3-dimmensional sphere as the set of quaternions of length one. The quaternion group induces on $\mathbb{S}^3$ a structure of noncommutative Lie group. This…

In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…

We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed…

The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U(2,1) and SU(2,1) are calculated. The results are obtained using the identification of these moduli spaces with moduli…