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.
A Weil Remarks on cohomology of groups Ann. of Math., 80 (1964), pp. 149-157 CrossrefGoogle Scholar Cited by (6) Isomorphism theory for orthogonal groups over arbitrary integral domains 1978, Journal of Algebra Invariant Conformal Killing–Yano 2-Forms on Five-Dimensional Lie Groups 2022, Jo...
denotes the lie algebra of g , and \(u_{\alpha } = \{x_{\alpha }(t) {\mid } t \in k\}\) is the root subgroup of g corresponding to a root \(\alpha \in \sigma (g)\) . if \(x \in g\) then \(t_x : g \rightarrow g\) is the inner automorphism of g induced ...
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 ...
Let G be a connected, complex, semi-simple Lie group Let g be an element in G. Let B be a Borel subgroup of G and g in B. Let m and n be the least positive integers such that the element gm lies on a one-parameter subgroup in G and the element gn lies on a one-parameter ...
Proof of(a). Here the approach is similar to other applications of Lie theory. (See, forexample, [2, Section 9].) We provide an outline. LetL¼LðGÞbe the Lie algebraofGand letL0¼XnANvðAdðnÞ1ÞL:Subgroups of algebraic groups which are clopen in theS-congruence...
Transitive linear groups and linear groups which contain irreducible subgroups of prime order II J. Algebra, 93 (1985), pp. 151-164 View PDFView articleView in ScopusGoogle Scholar 15 C. Hering, M.W. Liebeck, J. Saxl The factorizations of the finite exceptional groups of Lie type J. Alg...
and the associated entropy. Main results include a general scheme to produce such subgroups and a proof that the complement of the minimal ideal in a free profinite semigroup on more than one generator is closed under all implicit operations that do not lie in the minimal ideal and even unde...
This is the second paper in a series devoted to algorithmic problems [for the first one see J. Pure Appl. Algebra 39, 53-94 (1986; Zbl 0577.20021)]. Here the authors use a variation of O. Kharlampovich's example of a finitely presented g... ...
By C(M) and C[M] are denoted, respectively, the field of rational functions and the algebra of regular functions over the algebraic manifold M. By an irreducible representation of an algebraic group we shall always mean a finite-dimensional irreducible representation. The representation contra...