On the classification problem of the quasi-isomorphism classes of 1-connected minimal free cochain algebras |
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Authors: | Mahmoud Benkhalifa |
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Institution: | Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, PO Box 715, Mekkah, Saudi Arabia |
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Abstract: | The purpose of this paper is to classify the quasi-isomorphism classes of 1-connected minimal free cochain algebras over a commutative ring. Our tool to address this problem is a “certain” long sequence, called the Whitehead exact sequence, which we construct for every such algebra. We introduce the notion of coherent isomorphisms between these exact sequences and we show that two 1-connected minimal free cochain algebras are quasi-isomorphic if and only if their respective Whitehead exact sequences are coherently isomorphic. |
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Keywords: | primary 55Q15 secondary 55U99 |
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