June 2023 The homotopy Lie algebra of a Tor-independent tensor product
Luigi Ferraro, Mohsen Gheibi, David A. Jorgensen, Nicholas Packauskas, Josh Pollitz
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Illinois J. Math. 67(2): 383-407 (June 2023). DOI: 10.1215/00192082-10592402


In this article, we investigate a pair of surjective local ring maps S1RS2 and their relation to the canonical projection RS1RS2, where S1, S2 are Tor-independent over R. Our main result asserts a structural connection between the homotopy Lie algebra of S:=S1RS2, denoted π(S), in terms of those of R, S1, and S2; namely, π(S) is the pullback of (adjusted) Lie algebras along the maps π(Si)π(R) in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include structural results on André–Quillen cohomology, stable cohomology, and Tor algebras, as well as an equality relating the Poincaré series of the common residue field of R, S1, S2, and S.


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Luigi Ferraro. Mohsen Gheibi. David A. Jorgensen. Nicholas Packauskas. Josh Pollitz. "The homotopy Lie algebra of a Tor-independent tensor product." Illinois J. Math. 67 (2) 383 - 407, June 2023. https://doi.org/10.1215/00192082-10592402


Received: 20 July 2022; Revised: 12 January 2023; Published: June 2023
First available in Project Euclid: 18 April 2023

MathSciNet: MR4593896
zbMATH: 07724277
Digital Object Identifier: 10.1215/00192082-10592402

Primary: 13D02
Secondary: 13D07 , 16E45

Rights: Copyright © 2023 by the University of Illinois at Urbana–Champaign


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Vol.67 • No. 2 • June 2023
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