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On the subgroups of the centers of simply connected simple Lie groups : Classification of simple Lie groups in the largeopenaire +1 more source
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Embedding of a Simple Lie Group into a Simple Lie Group and Branching Rules
Journal of Mathematical Physics, 1967A criterion established by Dynkin is used to specify the embedding of a connected simple Lie group G′ into a connected simple Lie group G, and to derive a standard procedure for evaluating branching rules. It is shown that the weight systems of the irreducible parts contained in the representation of G′ induced by a given finite dimensional ...
Navon, A., Patera, J.
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Isoparity and Simple Lie Group
Journal of Mathematical Physics, 1967The 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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Projection operators for simple lie groups
Theoretical and Mathematical Physics, 1971Summary: 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. +2 more
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On simple lie groups of rank 3
Il Nuovo Cimento, 1965Properties 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, 1993It 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, 1958The 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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