Geodesic
Cartier isomorphism for unital associative algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 43-60

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Given an associative unital algebra $A$ over a perfect field $k$ of odd positive characteristic, we construct a noncommutative generalization of the Cartier isomorphism for $A$. The role of differential forms is played by Hochschild homology classes, and the de Rham differential is replaced with the Connes–Tsygan differential. 
@article{TM_2015_290_a3,
     author = {D. Kaledin},
     title = {Cartier isomorphism for unital associative algebras},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {43--60},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a3/}
}
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D. Kaledin. Cartier isomorphism for unital associative algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 43-60. http://geodesic.mathdoc.fr/item/TM_2015_290_a3/