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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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