Results 141 to 150 of about 1,304,850 (179)

Isoparity and Simple Lie Group

Journal of Mathematical Physics, 1967
The direct generalization of the isoparity (or G-parity), with the defining property that it is commutable with the referring internal symmetry group, is investigated on the basis of the theory of Lie algebra. This is one special problem of the group extension of a simple Lie group by an involution.
Tanabe, Kosai, Shima, Kazuhisa
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Elastic Helices in Simple Lie Groups

Journal of Lie Theory, 2015
Summary: Elastic curves (elastica) are classical variational objects with many applications in physics and engineering. Elastica in real space forms are well understood, but in other ambient spaces there are few known explicit examples, except geodesics.
Garay, Óscar J., Noakes, Lyle
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Projection operators for simple lie groups

Theoretical and Mathematical Physics, 1971
Summary: The solution of many problems in nuclear theory and elementary particle physics amounts to decomposing the reducible representations of the symmetry groups of quantum mechanical systems into irreducible components. To carry out this decomposition, projection operators are needed. In the present paper we have constructed, for all simple compact
Asherova, R. M., Smirnov, Yu. F., Tolstoĭ, V. N.   +2 more
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On simple lie groups of rank 3

Il Nuovo Cimento, 1965
Properties of simple Lie algebras of rank three, are investigated in view of physical applications; more precisely, dimensions, weight diagrams, decompositions with respect to regular subalgebras and decomposition of products of representations are given for the lowest order irreducible representations; we also explain somme techniques to deal with ...
Loupias, G., Sirugue, M., Trotin, J. C.
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Representations of simple lie groups

Reports on Mathematical Physics, 1993
It is known that the real homology \(H_ * (G)\) of a compact Lie group \(G\) is a Cartesian product of certain odd-dimensional spheres. In the author's interpretation, the group itself can be viewed as a ``twisted'' product of the same spheres: for instance, \(SU(3) \sim S^ 3 \times S^ 5\) is interpreted as the existence of the principal bundle \(SU(2)
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The Betti Numbers of the Simple Lie Groups

Canadian Journal of Mathematics, 1958
The purpose of the present paper1 is to simplify the calculation of the Betti numbers of the simple compact Lie groups.For the unimodular group and the orthogonal group on a space of odd dimension the form of the Poincaré polynomial was correctly guessed by E. Cartan in 1929 (5, p. 183). The proof of his conjecture and its extension to the four classes
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Branching Rules for Simple Lie Groups

Journal of Mathematical Physics, 1965
If 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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Construction of invariants for simple lie groups

Nuclear Physics, 1964
Abstract 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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Semigroups of Simple Lie Groups and Controllability

Journal of Dynamical and Control Systems, 2013
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Dynamics of Simple Lie Groups on Lorentz Manifolds

Geometriae Dedicata, 2004
In [``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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