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Resolutions for
twisted tensor products
Anne Shepler and Sarah Witherspoon |
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Vol. 298 (2019), No. 2, 445–469
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Abstract |
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We build resolutions for general twisted tensor products of algebras. These bimodule and module resolutions unify many constructions in the literature and are suitable for computing Hochschild (co)homology and more generally Ext and Tor for (bi)modules. We analyze in detail the case of Ore extensions, consequently obtaining Chevalley–Eilenberg resolutions for universal enveloping algebras of Lie algebras (defining the cohomology of Lie groups and Lie algebras). Other examples include semidirect products, crossed products, Weyl algebras, Sridharan enveloping algebras, and Koszul pairs. |
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Keywords
twisted tensor product, projective resolutions, Hochschild
(co)homology, augmented algebras
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Mathematical Subject Classification 2010
Primary: 16E05, 16E30, 16E40
Secondary: 16S30, 57T10
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Milestones
Received: 10 January 2017
Revised: 24 July 2018
Accepted: 25 July 2018
Published: 8 March 2019
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Authors |
| Anne Shepler | |
| Department of Mathematics University of North Texas Denton, TX United States |
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| Sarah Witherspoon | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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