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In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if acts freely on , then .
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We study Lie group structures on groups of the form C
∞(M, K), where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra
for which the evaluation map is smooth. We then prove the existence of such a structure if the universal cover of K is diffeomorphic to a locally convex space and if the image of the left logarithmic derivative in is a smooth submanifold, the latter being the case in particular if M is one-dimensional. We also obtain analogs of these results for the group of holomorphic maps on a complex manifold with values in a complex Lie group K. We further show that there exists a natural Lie group structure on if K is Banach and M is a non-compact complex curve with finitely generated fundamental group.
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Let K be a field of characteristic p>0 and let KG be the group algebra of an arbitrary group G over K. It is known that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p+1. The group algebras KG for which these indices are p+1 or 2p or 3p?1 or 4p?2 have already been determined. In this paper, we classify the group algebras KG for which the upper Lie nilpotency index is 5p?3, 6p?4 or 7p?5. 相似文献
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Xiaofei Qi 《Linear and Multilinear Algebra》2013,61(4):391-397
Let 𝒜 and ? be unital algebras over a commutative ring ?, and ? be a (𝒜,??)-bimodule, which is faithful as a left 𝒜-module and also as a right ?-module. Let 𝒰?=?Tri(𝒜,??,??) be the triangular algebra and 𝒱 any algebra over ?. Assume that Φ?:?𝒰?→?𝒱 is a Lie multiplicative isomorphism, that is, Φ satisfies Φ(ST???TS)?=?Φ(S)Φ(T)???Φ(T)Φ(S) for all S, T?∈?𝒰. Then Φ(S?+?T)?=?Φ(S)?+?Φ(T)?+?Z S,T for all S, T?∈?𝒰, where Z S,T is an element in the centre 𝒵(𝒱) of 𝒱 depending on S and T. 相似文献
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In this article, we determine the Cartan invariants for Zassenhaus algebras W(1,n). This is done by reducing representations of generalized restricted Cartan type Lie algebra W(1,n) to representations of restricted Lie algebras W(1,1) and of ± b𝔰 ± b𝔩(2), and then extending Feldvoss-Nakano's argument on W(1,1) to the case W(1,n). 相似文献
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In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi‐bounded (respectively, linear) o‐minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([2]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈Rm, +〉 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. 相似文献
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We classify group algebras of torsion groups over a field of characteristic with units satisfying a group identity.
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Jean-Louis Tu 《Transactions of the American Mathematical Society》2006,358(11):4721-4747
We show that Haefliger's cohomology for étale groupoids, Moore's cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (or Cech) cohomology for topological simplicial spaces.