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Group Cohomology and Lie Algebra Cohomology in Lie Groups. II
Indagationes Mathematicae (Proceedings), 1953W. T. V. Est
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1995
This chapter discusses the cohomology of groups. The cohomology of groups is one of the crossroads of mathematics. It has its origins in the representation theory, class field theory, and algebraic topology. The theory of cohomology of groups in degrees higher than two really begins with a theorem in algebraic topology.
Benson, D. J., Kropholler, P. H.
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This chapter discusses the cohomology of groups. The cohomology of groups is one of the crossroads of mathematics. It has its origins in the representation theory, class field theory, and algebraic topology. The theory of cohomology of groups in degrees higher than two really begins with a theorem in algebraic topology.
Benson, D. J., Kropholler, P. H.
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1971
In this chapter we shall apply the theory of derived functors to the important special case where the ground ring Λ is the group ring ℤ G of an abstract group G over the integers. This will lead us to a definition of cohomology groups H n (G, A) and homology groups H n (G, B), n ≧ 0, where A is a left and B a right G-module (we speak of “G-modules ...
Peter Hilton, Urs Stammbach
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In this chapter we shall apply the theory of derived functors to the important special case where the ground ring Λ is the group ring ℤ G of an abstract group G over the integers. This will lead us to a definition of cohomology groups H n (G, A) and homology groups H n (G, B), n ≧ 0, where A is a left and B a right G-module (we speak of “G-modules ...
Peter Hilton, Urs Stammbach
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Cohomology of groups and transfer
The Annals of Mathematics, 1953The purpose of this paper is to show how the transfer (Verlagerung) of a group A into a subgroup B of finite index can be obtained and generalized in the framework of the cohomology theory of groups (cf. [3]1) and of abstract complexes over a ring [2]. The generalized transfers are homomorphisms of the cohomology groups of the subgroup B into those of ...
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Applications of group cohomology to the classification of quasicrystal symmetries
, 2003In 1962, Bienenstock and Ewald described the classification of crystalline space groups algebraically in the dual, or Fourier, space. After the discovery of quasicrystals in 1984, Mermin and collaborators recognized in this description the principle of ...
Benji Fisher, D. Rabson
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Group cohomology and the symplectic structure on the moduli space of representations
, 1998The space of equivalence classes of irreducibleb representations of the fundamental group of a compact oriented surface of genus at least 2 in a Lie group has a natural symplectic form.
K. Guruprasad, C. Rajan
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