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On the indecomposable elements of the bar construction


Author: Richard M. Hain
Journal: Proc. Amer. Math. Soc. 98 (1986), 312-316
MSC: Primary 55U15; Secondary 18G10, 55P62
DOI: https://doi.org/10.1090/S0002-9939-1986-0854039-5
MathSciNet review: 854039
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Abstract: An explicit formula for a canonical splitting $ s:Q\mathcal{B}({\mathcal{E}^ \cdot }) \to \mathcal{B}({\mathcal{E}^ \cdot })$ of the projection $ \mathcal{B}({\mathcal{E}^ \cdot }) \to Q\mathcal{B}({\mathcal{E}^ \cdot })$ of the bar construction on a commutative d.g. algebra $ {\mathcal{E}^\cdot}$ onto its indecomposables is given. We prove that $ s$ induces a d.g. algebra isomorphism $ \Lambda (Q\mathcal{B}({\mathcal{E}^\cdot})) \to \mathcal{B}({\mathcal{E}^\cdot})$ and that $ H(Q\mathcal{B}({\mathcal{E}^\cdot}))$ is isomorphic with $ QH(\mathcal{B}({\mathcal{E}^\cdot}))$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0854039-5
Keywords: Bar construction
Article copyright: © Copyright 1986 American Mathematical Society

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