منابع مشابه
Questions on Lie Algebras of Cohomological Dimension 1
A Lie algebra L is said to be of cohomological dimension 1, if H(L, M) = 0 for any L-module M . Due to the standard interpretation of the second cohomology group, this is equivalent to the condition that each exact sequence 0 → M → G → L → 0 splits. Of course, the cohomological dimension may be defined via standard devices of homological algebra – e.g. as the minimal length of the projective re...
متن کاملAutomorphisms of Pro-p groups of finite virtual cohomological dimension
Let G be a pro-p group of finite cohomological dimension and type FP∞ and T is a finite p-group of automorphisms of G. We prove that the group of fixed points of T in G is again a pro-p group of type FP∞ (in particular it is finitely presented). Moreover we prove that a pro-p group G of type FP∞ and finite virtual cohomological dimension has finitely many conjugacy classes of finite subgroups.
متن کاملNormal subgroups of profinite groups of finite cohomological dimension
We study a profinite group G of finite cohomological dimension with (topologically) finitely generated closed normal subgroup N . If G is pro-p and N is either free as a pro-p group or a Poincaré group of dimension 2 or analytic pro-p, we show that G/N has virtually finite cohomological dimension cd(G) − cd(N). Some other cases when G/N has virtually finite cohomological dimension are considere...
متن کاملA Cohomological Characterization of Approximately Finite Dimensional Von Neumann Algebras
One of the purposes in the computation of cohomology groups is to establish invariants which may be helpful in the classification of the objects under consideration. In the theory of continuous Hochschild cohomology for operator algebras R. V. Kadison and J. R. Ringrose proved [10] that for any hyperfinite von Neumann algebra M and any dual normal M-bimodule S, all the continuous cohomology gro...
متن کاملOn Monomial Algebras of Finite Global Dimension
Let G be an associative monomial k-algebra. If G is assumed to be finitely presented, then either G contains a free subalgebra on two monomials or else G has polynomial growth. If instead G is assumed to have finite global dimension, then either G contains a free subalgebra or else G has a finite presentation and polynomial growth. Also, a graded Hopf algebra with generators in degree one and r...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1971
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000014409