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Classification of almost spherical pairs of compact simple Lie groups

Ihor Mykytyuk, Anatoly Stepin (2000)

Banach Center Publications

All homogeneous spaces G/K (G is a simple connected compact Lie group, K a connected closed subgroup) are enumerated for which arbitrary Hamiltonian flows on T*(G/K) with G-invariant Hamiltonians are integrable in the class of Noether integrals and G-invariant functions.

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a unimodular connected solvable Lie group with center Z such that for some in the Lie algebra h of H , the symplectic for B on h / z given by ( [ x , y ] ) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z , such that the center of G / Rad G is finite, has discrete series if and only if G may be written as G = H S ' , H S = Z 0 , where H is a H -group with...

Classification of self-dual torsion-free LCA groups

S. Wu (1992)

Fundamenta Mathematicae

In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded as an open...

Clifford approach to metric manifolds

Chisholm, J. S. R., Farwell, R. S. (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis { e j : j = 1 , , n } satisfying the condition { e i , e j } e i e j = e j e i = 2 I η i j , where I denotes the unit scalar of the algebra and ( η i j ) the nonsingular Minkowski...

Closed subgroups in Banach spaces

Fredric Ancel, Tadeusz Dobrowolski, Janusz Grabowski (1994)

Studia Mathematica

We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of c 0 . Other results on subgroups of linear spaces are obtained.

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