We also determine the fixed point\nsubgroup $\\Aut(\\fru_0)^\\Gamma$.Jing-Song HuangJun YuHuang, Jing Song, and J. Yu. Klein four-subgroups of Lie algebra automorphisms, Pacific Journal of Mathematics 262.2(2011):397-420.
By calculating the symmetric subgroups $\Aut(\fru_0)^{heta}$ and their involution classes, we classify the Klein four subgroups $\Gamma$ of $\Aut(\fru_0)$ for each compact simple Lie algebra $\fru_0$ up to conjugation. This leads to a new approach of classification of semisimple symme...
Next we turn to real Lie groups. Chevalley's complex formulation of Tannaka's duality theorem states that if G is a compact real Lie group, then the universal complexification G of G is isomorphic with the group A(G) of all proper automorphisms of the algebra R(G) of representative ...
Berry's phase for compact Lie groups The Lie group adiabatic evolution determined by a Lie algebra parameter\ndependent Hamiltonian is considered. It is demonstrated that in the case when\nthe parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its\nfundam... E Strahov 被引...
摘要: LetGbe a connected, simply connected, simple complex algebraic group and letbe a primitiveth root of one,odd and 3ifGis of typeG2. We determine all Hopf algebra quotients of the quantized coordinate algebra(G).关键词: quantum groups quantized enveloping algebras quantized coordinate ...
on extensions of vector groups by compact groups, and of several results obtained in the previous chapters, notably the decomposition Ad g = ω K × P , and the conjugacy of maximal compact subgroups in Aut \(\mathfrak{g}\) , where \(\mathfrak{g}\) is a semisimple Lie algebra. In...
Automorphism subgroups of the free lie algebra of rank 31-cocyclesplit extensionconjugacy classes of subgroupsfree Lie algebraautomorphism groupLet F r be a free Lie algebra over the field . We give an example of some subgroup of Aut F r that is isomorphic to a subgroup of * but not ...
Previtali,Andrea - 《Communications in Algebra》 被引量: 6发表: 1999年 Subspace stabilizers and maximal subgroups of exceptional groups of Lie type In 1998, Liebeck and Seitz introduced a constant t(G) t(G) , dependent on the root system of a reductive algebraic group G G and proved that...
PB Kleidman - 《Journal of Algebra》 被引量: 430发表: 1987年 The Maximal Subgroups of the Low-Dimensional Finite Classical Groups: Foreword Let p be a prime number, q=p n . Let G 0 =PΩ 8 + (q)D 4 (q) be the simple Chevalley group of type D 4 over the field of q elements...
Let $G$ be a simple algebraic group over an algebraically closed field $K$ with Lie algebra $\\mathfrak{g}$. For unipotent elements $u \\in G$ and nilpotent elements $e \\in \\mathfrak{g}$, the Jordan block sizes of $\\operatorname{Ad}(u... M Korhonen 被引量: 0发表: 2023...