منابع مشابه
On Torsion Subgroups of Lie Groups
We are concerned with torsion subgroups of Lie groups. We extend the classical result of C. Jordan on the structure of finite linear groups to torsion subgroups of connected Lie groups. 1. In [1], Boothby and Wang proved that, for any connected Lie group G, there exists a number k{G) such that any finite subgroup contains an abelian normal subgroup whose index is bounded by k{G), thereby genera...
متن کاملHigher torsion in p-groups, Casimir operators and the classifying spectral sequence of a Lie algebra
We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E r [g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the corresponding group in characteristic p. This spectral sequence is then studied for complex semisimple Lie algebras like sln(C), and the results there are transferred to...
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In this note, G is a compact connected Lie group. We are concerned with the torsion of the cohomology ring H*(G; Z) of G over the integers, certain commutative subgroups of G, and relations between these two questions. NOTATION. E(mi, • • • , mr) or £ A ( ^ I , • • • , mr) denotes the exterior algebra over the ring A of a free .4-module with r generators of respective degrees wi, • • • , mr; p ...
متن کاملOn Torsion-free Abelian Groups and Lie Algebras
It is known that many of the classes of simple Lie algebras of prime characteristic of nonclassical type have simple infinite-dimensional analogues of characteristic zero (see, for example, [4, p. 518]). We consider here analogues of those algebras which are defined by a modification of the definition of a group algebra. Thus we consider analogues of the Zassenhaus algebras as generalized by Al...
متن کاملHyperkähler Torsion Structures Invariant by Nilpotent Lie Groups
We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on R which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex struc...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1998
ISSN: 0025-5645
DOI: 10.2969/jmsj/05040801