Corings, their dual rings and relative (co)Hochschild cohomology

2025/08/14 by Lindell, Jonathan
#16E40 (Primary) 16T15 #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.10668

Abstract

We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level of B_∞-algebras of the chain complexes, by showing that the opposite B_∞-algebra of the relative Hochschild cochains of the right algebra is isomorphic to the B_∞-algebra of Cartier cochains. Lastly, we apply this to entwining structures where the coalgebra is finite-dimensional, to get a description of the equivariant cohomology of the entwining structure as the relative Hochschild cohomology of the twisted convolution algebra.

Citations

• Strongly stratifying ideals, Morita contexts and Hochschild homology
• Leavitt path algebras, B_∞-algebras and Keller's conjecture for singular Hochschild cohomology
• Deformations of path algebras of quivers with relations
• The first Hochschild (co)homology when adding arrows to a bound quiver algebra
• Deleting or adding arrows of a bound quiver algebra and Hochschild (co)homology
• Gerstenhaber bracket on the Hochschild cohomology via an arbitrary\n resolution
• In the bocs seat: Quasi-hereditary algebras and representation type
• Infinity inner products on A-infinity algebras
• The cohomology structure of an algebra entwined with a coalgebra
• Operads, homotopy algebra and iterated integrals for double loop spaces

Related

• The cohomology structure of an algebra entwined with a coalgebra
• Cyclic Cohomology of Corings
• Simplicial Hochschild cochains as an Amitsur complex
• On the cohomology of a Galois entwining
• The Hochschild cohomology ring of the singular cochain algebra of a space