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Description: |
The aim of this talk is to give an intrinsic version of the Schreier-Mac Lane extension theorem, classically known for groups: on the set Ext(Y,K) of isomorphism classes of extensions with fixed abstract kernel there is a simply transitive action of the abelian group Ext(Y,ZK), where ZK is the center of K and the abstract kernel of these last extensions is iduced by tre previous one. D. Bourn showed that this result holds in any semi-abelian action representative category. This setting, however, excludes many interesting algebraic structures, like the category of rings. In the present talk we show that the same Schreier-Mac Lane extension theorem holds in a much wider class of categories, called action accessible categories, provided they are Barr-exact. This family of categories includes, beyond groups and Lie algebras, the categories of rings, associative algebras, Poisson algebras, Leibniz algebras, associative dialgebras (in the sense of J.L. Loday) and any variey of groups.
(Joint work with Dominique Bourn.)
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Date: |
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| Start Time: |
15:30 |
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Speaker: |
Andrea Montoli (CMUC)
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Institution: |
CMUC
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Place: |
Sala 5.5
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| Research Groups: |
-Algebra, Logic and Topology
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See more:
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<Main>
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