NDLI: Baer Invariants and Cohomology of Precrossed Modules

Content Provider	Springer Nature Link
Author	Arias, Daniel Ladra, Manuel
Copyright Year	2013
Abstract	In this paper we study Baer invariants of precrossed modules relative to the subcategory of crossed modules, following Fröhlich and Furtado-Coelho’s general theory on Baer invariants in varieties of Ω-groups and Modi’s theory on higher dimensional Baer invariants. Several homological invariants of precrossed and crossed modules were defined in the last two decades. We show how to use Baer invariants in order to connect these various homology theories. First, we express the low-dimensional Baer invariants of precrossed modules in terms of a new non-abelian tensor product of a precrossed module. This expression is used to analyze the connection between the Baer invariants and the homological invariants of precrossed modules defined by Conduché and Ellis. Specifically we prove that the second homological invariant of Conduché and Ellis is in general a quotient of the first component of the Baer invariant we consider. The definition of classical Baer invariants is generalized using homological methods. These generalized Baer invariants of precrossed modules are applied to the construction of five term exact sequences connecting the generalized Baer invariants with the cohomology theory of crossed modules considered by Carrasco, Cegarra and R.-Grandjeán and the cohomology theory of precrossed modules.
Ending Page	304
Page Count	16
Starting Page	289
File Format	PDF
ISSN	09272852
e-ISSN	15729095
Journal	Applied Categorical Structures
Issue Number	1
Volume Number	22
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-04-12
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Crossed module Homological methods in group theory Geometry Precrossed module Baer invariant Central extension Convex and Discrete Geometry Non-Abelian tensor product Nonabelian homological algebra Theory of Computation Cohomology Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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