Related papers: Automorphisms of toroidal Lie superalgebras

Let $A$ be one of the following Clifford algebras : $\mathbb{R}_2 \cong \mathbb{H}$ or $\mathbb{R}_3$. For the algebra $A$, the automorphism group $Aut(A)$ and its invariants are well known. In this paper we will describe the invariants of…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…

We prove that every automorphism of the restricted root system of a real semisimple Lie algebra -- when defined properly -- can be lifted to an automorphism of that Lie algebra. In particular, this can be applied to automorphisms of the…

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…

Let ${\mathfrak g}$ be a complex simple Lie algebra with Borel subalgebra ${\mathfrak b}$. Consider the semidirect product $I{\mathfrak b}={\mathfrak b}\ltimes{\mathfrak b}^*$, where the dual ${\mathfrak b}^*$ of ${\mathfrak b}$, is…

We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present a method to explicitly obtain generating sets, and prove a…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

In a previous paper we have classified the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this work we give a geometrical description of such varieties. In particular, we determine their group of…

It is known that simple algebraic groups of type $F_4$ defined over a field $k$ are precisely the full automorphism groups of Albert algebras over $k$. We explore $R$-triviality for the group $\text{\bf Aut}(A)$ when $A$ is an Albert…

We consider possibly singular rational projective k*-surfaces and provide an explicit description of the unit component of the automorphism group in terms of isotropy group orders and intersection numbers of suitable invariant curves. As an…

The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given…

In previous work, the author proved that there is a countably infinite family of N=2 superconformal equivalence classes of DeWitt N=2 superconformal super-Riemann surfaces with closed, genus-zero body. In this paper, we determine the…

Let $0 \to A \to L \to B \to 0$ be a short exact sequence of Lie algebras over a field $F$, where $A$ is abelian. We show that the obstruction for a pair of automorphisms in $\Aut(A) \times \Aut(B)$ to be induced by an automorphism in…

Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…

We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra $A_1$. The list we obtain turns out to be discrete and for example, the only non-solvable Lie algebras…

In this paper, we determine derivations of Borel subalgebras and their derived subalgebras called nilradicals, in Kac-Moody algebras (and contragredient Lie algebras) over any field of characteristic 0; and we also determine automorphisms…