Cyclic cohomology and algebra extensions

DOI10.1007/BF00533370zbMath0696.16021OpenAlexW2070050880MaRDI QIDQ910472

Daniel Quillen

Publication date: 1989

Published in: \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00533370

zbMATH Keywords

spectral sequencecyclic cohomologybar constructionChern-Simons formConnes classes

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Grothendieck groups, (K)-theory, etc. (16E20) Spectral sequences, hypercohomology (18G40) Centralizing and normalizing extensions (16S20)

Related Items (26)

Some aspects of homotopic algebra and non-abelian (co)homology theories ⋮ Bivariant cyclic cohomology and models for cyclic homology types ⋮ Cyclic and Hochschild homology of 2-nilpotent algebras ⋮ Fine Hochschild invariants of derived categories for symmetric algebras ⋮ Dimension quotients, Fox subgroups and limits of functors ⋮ Hopf type formulas for cyclic homology ⋮ Stable invariance of the restricted Lie algebra structure of Hochschild cohomology ⋮ Cyclic cohomology and algebra extensions ⋮ Derived representation schemes and cyclic homology ⋮ Quillen's work on the foundations of cyclic cohomology ⋮ Cyclic cohomology after the excision theorem of Cuntz and Quillen ⋮ Global Hochschild (co-)homology of singular spaces ⋮ A bivariant Chern character for \(p\)-summable quasihomomorphisms ⋮ Cyclic homologies of crossed modules of algebras ⋮ A higher limit approach to homology theories ⋮ A limit approach to group homology. ⋮ A∞-modules and Calogero-Moser spaces ⋮ Cyclic Homology and Nonsingularity ⋮ Cyclic homology, tight crossed products, and small stabilizations ⋮ Limits over categories of extensions. ⋮ HIGHER TRACES ON GROUP RINGS ⋮ Homology of Centralizers ⋮ Algebra cochains and cyclic cohomology ⋮ \(A_{\infty}\)-coderivations and the Gerstenhaber bracket on Hochschild cohomology ⋮ Higher colimits, derived functors and homology ⋮ Relative cyclic homology of square zero extensions

Cites Work

• Relative algebraic K-theory and cyclic homology
• Excision in cyclic homology and in rational algebraic K-theory
• Algebra cochains and cyclic cohomology
• Cyclic cohomology and algebra extensions
• Caractère de Chern bivariant. (Bivariant Chern character)
• Cyclic homology and the Lie algebra homology of matrices
• Cyclic homology, derivations, and the free loopspace
• Non-commutative differential geometry
• Cyclic homology of enveloping algebras
• Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity)
• Differential homological algebra and homogeneous spaces
• Introduction to Algebraic K-Theory. (AM-72)
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