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Transactions of the American Mathematical Society

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Uniqueness of product and coproduct decompositions in rational homotopy theory


Authors: Roy Douglas and Lex Renner
Journal: Trans. Amer. Math. Soc. 264 (1981), 165-180
MSC: Primary 55P62
MathSciNet review: 597874
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Abstract: Let $ X$ be a nilpotent rational homotopy type such that (1) $ S(X)$, the image of the Hurewicz map has finite total rank, and (2) the basepoint map of $ M$, a minimal algebra for $ X$, is an element of the Zariski closure of $ {\text{Aut}}(M)$ in $ {\text{End}}(M)$ (i.e. $ X$ has "positive weight"). Then (A) any retract of $ X$ satisfies the two properties above, (B) any two irreducible product decompositions of $ X$ are equivalent, and (C) any two irreducible coproduct decompositions of $ X$ are equivalent.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0597874-3
Keywords: Minimal algebra, rational homotopy, $ I$-split category, idempotent, positive weight, algebraic group, toroidal imbedding
Article copyright: © Copyright 1981 American Mathematical Society