Research Catalog

Title

Cyclic homology / Jean-Louis Loday.

Author

Loday, Jean-Louis.

Publication

Berlin ; New York : Springer-Verlag, 1992.

Items in the Library & Off-site

Details

Description

xvi, 454 pages : illustrations; 24 cm.

Series Statement

Grundlehren der mathematischen Wissenschaften ; 301

Uniform Title

Grundlehren der mathematischen Wissenschaften ; 301.

Subject

• Homology theory
• 31.27 category theory (mathematics)
• 31.61 algebraic topology
• Homology theory
• Zyklische Homologie
• Homologische algebra
• Homologie

Bibliography (note)

• Includes bibliographical references (p. 431]-444) and index.

Contents

• Ch. 1. Hochschild Homology -- 1.0. Chain Complexes -- 1.1. Hochschild Homology -- 1.2. The Trace Map and Morita Invariance -- 1.3. Derivations, Differential Forms -- 1.4. Nonunital Algebras and Excision -- 1.5. Hochschild Cohomology, Cotrace, Duality -- 1.6. Simplicial Modules -- Ch. 2. Cyclic Homology of Algebras -- 2.1. Definition of Cyclic Homology -- 2.2. Connes' Exact Sequence, Morita Invariance, Excision -- 2.3. Differential Forms, de Rham Cohomology -- 2.4. Cyclic Cohomology -- 2.5. Cyclic Modules -- 2.6. Non-commutative Differential Forms -- Ch. 3. Smooth Algebras and Other Examples -- 3.1. Tensor Algebra -- 3.2. Symmetric Algebras -- 3.3. Universal Enveloping Algebras of Lie Algebras -- 3.4. Smooth Algebras -- 3.5. Andre-Quillen Homology -- 3.6. Deligne Cohomology -- Ch. 4. Operations on Hochschild and Cyclic Homology -- 4.1. Conjugation and Derivation -- 4.2. Shuffle Product in Hochschild Homology -- 4.3. Cyclic Shuffles and Kunneth Sequence for HC -- 4.4. Product, Coproduct in Cyclic Homology -- 4.5. [lambda]-Decomposition for Hochschild Homology -- 4.6. [lambda]-Decomposition for Cyclic Homology -- Ch. 5. Variations on Cyclic Homology -- 5.1. The Periodic and Negative Theories -- 5.2. Dihedral and Quaternionic Homology -- 5.3. Differential Graded Algebras -- 5.4. Commutative Differential Graded Algebras -- 5.5. Bivariant Cyclic Cohomology -- 5.6. Topological Algebras, Entire Cyclic Cohomology
• Ch. 6. The Cyclic Category, Tor and Ext Interpretation -- 6.1. Connes Cyclic Category [Delta]C and the Category [Delta]S -- 6.2. Tor and Ext Interpretation of HH and HC -- 6.3. Crossed Simplicial Groups -- 6.4. The Category of Finite Sets and the [lambda]-Decomposition -- Ch. 7. Cyclic Spaces and S[superscript 1]-Equivariant Homology -- 7.1. Cyclic Sets and Cyclic Spaces -- 7.2. Cyclic Homology and S[superscript 1]-Equivariant Homology -- 7.3. Examples of Cyclic Sets and the Free Loop Space -- 7.4. Hochschild Homology and Cyclic Homology of Group Algebras -- Ch. 8. Chern Character -- 8.1. The Classical Chern Character a la Chern-Weil -- 8.2. The Grothendieck Group K[subscript 0] -- 8.3. The Chern Character from K[subscript 0] to Cyclic Homology -- 8.4. The Dennis Trace Map and the Generalized Chern Character -- 8.5. The Bass Trace Conjecture and the Idempotent Conjecture -- Ch. 9. Classical Invariant Theory -- 9.1. The Fundamental Theorems of Invariant Theory -- 9.2. Coinvariant Theory and the Trace Map -- 9.3. Cayley-Hamilton and Amitsur-Levitzki Formulas -- 9.4. Proofs of the Fundamental Theorems -- 9.5. Invariant Theory for the Orthogonal and Symplectic Groups -- Ch. 10. Homology of Lie Algebras of Matrices -- 10.1. Homology of Lie Algebras -- 10.2. Homology of the Lie Algebra gl(A) -- 10.3. Stability and First Obstruction to Stability -- 10.4. Homology with Coefficients in the Adjoint Representation -- 10.5. The Symplectic and Orthogonal Cases
• 10.6. Non-commutative Homology of the Lie Algebra of Matrices -- Ch. 11. Algebraic K-Theory -- 11.1. The Bass-Whitehead Group K[subscript 1] and the Milnor Group K[subscript 2] -- 11.2. Higher Algebraic K-Theory -- 11.3. Algebraic K-Theory and Cyclic Homology of Nilpotent Ideals -- 11.4. Absolute and Relative Chern Characters -- 11.5. Secondary Characteristic Classes -- Ch. 12. Non-commutative Differential Geometry -- 12.1. Foliations and the Godbillon-Vey Invariant -- 12.2. Fredholm Modules and Index Theorems -- 12.3. Novikov Conjecture on Higher Signatures -- 12.4. The K-Theoretic Analogue of the Novikov Conjecture. App. A. Hopf Algebras -- App. B. Simplicial -- App. C. Homology of Discrete Groups and Small Categories -- App. D. Spectral Sequences -- App. E. Smooth Algebras / Maria O. Ronco.

ISBN

• 0387533397
• 9780387533391
• 3540533397
• 9783540533399

LCCN

92034146

OCLC

• ocm26674276
• 26674276
• SCSB-1967239

Owning Institutions

Princeton University Library