Algebra Structures on the Twisted Eilenberg-Zilber Theorem

Let G, G′, and G × τ  G′ be three simplicial groups (not necessarily abelian) and C N (G) ⊗ t  C N (G′) be the "twisted" tensor product associated to C N (G × τ  G′) by the twisted Eilenberg-Zilber theorem. Here we prove that the pair (C N (G) ⊗ t  C N (G′), μ) is a DGA-algebra where μ is...

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Bibliographic Details
Published in:Communications in algebra 2007-10, Vol.35 (11), p.3273-3291
Main Authors: Álvarez, V., Armario, J. A., Frau, M. D., Real, P.
Format: Article
Language:English
Subjects:
Contraction
Eilenberg-Zilber theorem
Homological perturbation lemma
Simplicial groups
Twisted cartesian product
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Summary:Let G, G′, and G × τ  G′ be three simplicial groups (not necessarily abelian) and C N (G) ⊗ t  C N (G′) be the "twisted" tensor product associated to C N (G × τ  G′) by the twisted Eilenberg-Zilber theorem. Here we prove that the pair (C N (G) ⊗ t  C N (G′), μ) is a DGA-algebra where μ is the standard product of C N (G) ⊗ C N (G′). Furthermore, the injection of the twisted Eilenberg-Zilber contraction is a DGA-algebra morphism and the projection and the homotopy operator satisfy other weaker multiplicative properties.
ISSN:0092-7872
1532-4125
DOI:10.1080/00914030701410369