Higher central extensions and cohomology

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• 作者：Diana Rodelo^a ; ^b ; ¹ ; ^{drodelo@ualg.pt" class="auth_mail" title="E-mail the corresponding author} ; Tim Van der Linden^b ; ^c ; ² ; ^{tim.vanderlinden@uclouvain.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：18G50 ; 18G60 ; 18G15 ; 20J ; 55N
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：10 January 2016
• 年：2016
• 卷：287
• 期：Complete
• 页码：31-108
• 全文大小：1150 K

文摘

We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between “internal” homology and “external” cohomology in semi-abelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators.