Related papers: Reality of Unipotent elements in Classical Lie Gro…

The paper concerns two versions of the notion of real forms of Lie superalgebras. One is the standard approach, where a real form of a complex Lie superalgebra is a real Lie superalgebra such that its complexification is the original…

In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all…

The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.

The goal of this paper is to show that many key results found in the study of Einstein Lorentzian nilpotent Lie algebras can still hold in the more general settings of unimodular Lie algebras and (completely) solvable Lie algebras.

It is shown that a unified description of classical and `quantum mechanical' gravity in its linearized form is possible.

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…

This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic two. Any non-trivial self-dual irreducible $K[G]$-module $W$ admits a non-degenerate $G$-invariant alternating bilinear form, thus giving a…

We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely,…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p > 0$. We consider connected reductive subgroups $X$ of $G$ that contain a given distinguished unipotent element $u$ of $G$. A result of…

The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

The classical approximation may be applied to a number of problems in non-equilibrium field theory. The principles and limits of classical real-time lattice simulations are presented, with particular emphasis on the definition of particle…

Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…

We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…

We classify all real and strongly real classes of the finite special unitary group $SU_n(q)$. Unless $q \equiv 3 (mod 4)$ and $n |4$, the classification of real classes is similar to that of the finite special linear group $SL_n(q)$. We…

Uninorms play a prominent role both in the theory and the applications of Aggregations and Fuzzy Logic. In this paper the class of group-like uninorms is introduced and characterized. First, two variants of a general construction -- called…

We provide a novel construction of quantized universal enveloping $*$-algebras of real semisimple Lie algebras, based on Letzter's theory of quantum symmetric pairs. We show that these structures can be `integrated', leading to a…

One interpretation of how the classical world emerges from an underlying quantum reality involves the build-up of certain robust entanglements between particles due to scattering events [Science Vol.301 p.1081]. This is an appealing view…