TY - GEN
T1 - On noncommutative differential forms
AU - Tsygan, Boris
N1 - Publisher Copyright:
© 2024 American Mathematical Society
PY - 2024
Y1 - 2024
N2 - We review the topic of noncommutative differential forms, following the works of Karoubi, Cuntz–Quillen, Cortiñas, Ginzburg–Schedler, and Waikit Yeung. In particular we give a new proof of the theorem of Ginzburg and Schedler that compares extended noncommutative De Rham cohomology to cyclic homology. This theorem is a stronger version of a theorem of Karoubi. Wealso describe an algebraic structure, namely a category in DG cocategories, that noncommutative forms and other versions of noncommutative calculus are particular cases of.
AB - We review the topic of noncommutative differential forms, following the works of Karoubi, Cuntz–Quillen, Cortiñas, Ginzburg–Schedler, and Waikit Yeung. In particular we give a new proof of the theorem of Ginzburg and Schedler that compares extended noncommutative De Rham cohomology to cyclic homology. This theorem is a stronger version of a theorem of Karoubi. Wealso describe an algebraic structure, namely a category in DG cocategories, that noncommutative forms and other versions of noncommutative calculus are particular cases of.
KW - Hochschild and cyclic homology
KW - noncommutative differential forms
UR - http://www.scopus.com/inward/record.url?scp=85204683028&partnerID=8YFLogxK
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U2 - 10.1090/conm/802/16070
DO - 10.1090/conm/802/16070
M3 - Conference contribution
AN - SCOPUS:85204683028
SN - 9781470471422
T3 - Contemporary Mathematics
SP - 1
EP - 22
BT - Higher Structures in Topology, Geometry, and Physics - AMS Special Session Higher Structures in Topology, Geometry, and Physics, 2022
A2 - Kaufmann, Ralph M.
A2 - Markl, Martin
A2 - Voronov, Alexander A.
PB - American Mathematical Society
T2 - AMS Special Session on Higher Structures in Topology, Geometry, and Physics, 2022
Y2 - 26 March 2022 through 27 March 2022
ER -