additive K-theory

Term **additive K-theory** is a synonym for cyclic homology, used in early articles mainly of Russian and a bit by French school.

**Additive K-theory** is also a title of a historical article

- Boris Tsygan, Boris Feigin,
*Additive K-theory*, in K-theory, arithmetic and geometry, LNM 1289 (1987), edited by Yu. I. Manin, pp. 67–209, seminar 1984-1986 in Moscow), MR89a:18017

The additive K-theory is here studied in relation to the algebraic K-theory and Hochschild homology. Like there is a K-theory spectrum, one also constructs an additive K-theory/cyclic homology spectrum.

Contents of Tsygan-Feigin

- Introduction.
- Ch. 1. Additive K-functors.
- Ch. 2. Derived functors and relative additive K-functors.
- Ch. 3. Generalized free products.
- Ch. A. Lie algebra homology.
- Ch. 5. Operations in additive K-theory.
- Ch. 6. Additive K-functors of the commutative noetherian algebras.
- Ch. 7. Characteristic classes.
- Appendix. Cyclic objects.

There is also the related article

- Б. Л. Фейгин, Б. Л. Цыган, “Аддитивная K-теория и кристальные когомологии”, Функц. анализ и его прил., 19:2 (1985), 52–-62, pdf, MR88e:18008; Engl. transl. in B. L. Feĭgin, B. L. Tsygan,
*Additive $K$-theory and crystalline cohomology*, Functional Analysis and Its Applications, 1985, 19:2, 124–132.

Revised on December 2, 2010 19:35:01
by Zoran Škoda
(161.53.130.104)