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Semigroups of Simple Lie Groups and Controllability
Journal of Dynamical and Control Systems, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Homotopy Type of Lie Semigroups in Semi-Simple Lie Groups
Monatshefte f�r Mathematik, 2002Let \(G\) be a semisimple Lie group with finite center and \(S\subseteq G\) a subsemigroup with non-empty interior. The authors show that if \(S\) is generated by one-parameter semigroups, then there exists a compact subgroup of \(G\) whose homotopy groups are precisely the homotopy groups of \(S\).
San Martin, Luiz A. B. +1 more
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Construction of invariants for simple lie groups
Nuclear Physics, 1964Abstract A coupling coefficient for the orthogonal and symplectic groups is defined.It can be utilized to construct a set of invariants and it is proved that these are all the independent invariants of the considered groups excepting the orthogonal group in even dimensions for which an invariant cannot be constructed in a similar way.
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Branching Rules for Simple Lie Groups
Journal of Mathematical Physics, 1965If Γ is an irreducible representation of a group 𝒢, and ℋ is a subgroup of 𝒢, then Γ furnishes a representation of ℋ which is, in general, reducible, and the branching rules specify which irreducible representations of ℋ occur in the decomposition of this representation.
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Finite simple unisingular groups of Lie type
Journal of Group Theory, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guralnick, Robert M., Pham Huu Tiep
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A Poisson Formula for Semi-Simple Lie Groups
The Annals of Mathematics, 1963for some bounded function h on the boundary of the disc. The function h(z) determines a function h(g) on G by setting h(g) = h(g(O)). If h(z) is harmonic, it may be shown that h(g) is annihilated by a certain class of differential operators on G. The Poisson formula (1) may be used to express h(g), and we find that here it takes on a particularly ...
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The Demazure–Tits subgroup of a simple Lie group
Journal of Mathematical Physics, 1988The Demazure–Tits subgroup of a simple Lie group G is the group of invariance of Clebsch–Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure–Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of
Michel, L., Patera, J., Sharp, R. T.
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Commutators in Finite Simple Groups of Lie Type
Bulletin of the London Mathematical Society, 2000Summary: Using properties of the Steinberg character, we obtain a congruence modulo \(p\) for the number of ways in which a \(p\)-regular element may be expressed as a commutator in a finite simple group \(G\) of Lie type of characteristic \(p\). This congruence shows that such an element is a commutator in \(G\).
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Dynamics of Simple Lie Groups on Lorentz Manifolds
Geometriae Dedicata, 2004In [``Noncompact simple automorphism groups of Lorentz manifolds and other geometric manifolds'', Ann. Math. (2) 144, No. 3, 611--640 (1996; Zbl 0871.53048)], \textit{N. Kowalsky} proved that a connected simple Lie group with finite center acting nontriavially, nonproperly and isometrically on a connected Lorentz manifold is locally isomorphic to ...
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