Английская Википедия:Additive K-theory
In mathematics, additive K-theory means some version of algebraic K-theory in which, according to Spencer Bloch, the general linear group GL has everywhere been replaced by its Lie algebra gl.[1] It is not, therefore, one theory but a way of creating additive or infinitesimal analogues of multiplicative theories.
Formulation
Following Boris Feigin and Boris Tsygan,[2] let <math> A </math> be an algebra over a field <math> k </math> of characteristic zero and let <math> {\mathfrak gl}(A) </math> be the algebra of infinite matrices over <math>A</math> with only finitely many nonzero entries. Then the Lie algebra homology
- <math> H_\cdot ({\mathfrak gl}(A),k) </math>
has a natural structure of a Hopf algebra. The space of its primitive elements of degree <math> i</math> is denoted by <math>K^+_i(A)</math> and called the <math>i</math>-th additive K-functor of A.
The additive K-functors are related to cyclic homology groups by the isomorphism
- <math> HC_i(A) \cong K^+_{i+1}(A). </math>
References
- ↑ Шаблон:Cite journal
- ↑ B. Feigin, B. Tsygan. Additive K-theory, LNM 1289, Springer
