The group SU(3) is parameterized in terms of generalized “Euler angles”. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.

Suppose that an automorphism group G acts flag-transitively on a finite generalized hexagon or octagon S, and suppose that the action on both the point and line set is primitive. We show that G is an almost simple group of Lie type, that is, the socle of G is a simple Chevalley group.

suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

Electromagnetism can be generalized to Yang–Mills theory by replacing the group U(1) by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of ‘higher-dimensional Yang–Mills theory’. It turns out that to do this, one should replace the Lie group by a ‘Lie 2-group’, which is a category C where the set of objects and the set o...

A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with a first order symmetry on solutions of the Yang-Mills equations. Let g = g1+ · · ·+gn be the decomposition of the Lie algebra g of the structure group into ...

We provide an explicit description of symplectic leaves of a simply connected connected semisimple complex Lie group equipped with the standard Poisson-Lie structure. This sharpens previously known descriptions of the symplectic leaves as connected components of certain varieties. Our main tool is the machinery of twisted generalized minors. They also allow us to present several quasi-commuting...

Abstract. In this paper we explore the computation of the matrix exponential in a manner that is consistent with Lie-group structure. Our point of departure is the method of generalized polar decompositions, which we modify and combine with similarity transformations that bring the underlying matrix to a form more amenable to efficient computation. We develop techniques valid for a range of Lie...

We show that each triangular Poisson Lie group can be decomposed into Poisson submanifolds each of which is a quotient of a symplectic manifold. The Marsden–Weinstein–Meyer symplectic reduction technique is then used to give a complete description of the symplectic foliation of all triangular Poisson structures on Lie groups. The results are illustrated in detail for the generalized Jordanian P...