Simplicial and crossed resolutions of commutative algebras (Q1913961)
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scientific article; zbMATH DE number 883768
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Simplicial and crossed resolutions of commutative algebras |
scientific article; zbMATH DE number 883768 |
Statements
Simplicial and crossed resolutions of commutative algebras (English)
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9 July 1996
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The authors relate \textit{M. André}'s construction [``Homologie des algèbres commutatives'', Grundlehren 206 (1974; Zbl 0284.18009)] of the simplicial resolution of an algebra to an obvious construction of its crossed resolution [\textit{T. Porter}, J. Algebra 109, 415-429 (1987; Zbl 0619.16033)]. This construction does give a ``step-by-step'' construction of a crossed resolution, and an explicit description of this in low dimensions is presented. Thus, ``combinatorial algebra theory'' by analogy with ``combinatorial group theory'' contains some important new ideas.
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crossed module
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simplicial resolution of algebra
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Moore complex
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Peiffer element
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crossed resolution
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combinatorial algebra theory
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crossed complex
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