Additive K-theory
Introduction 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some version of algebraic K-theory in which, according to Spencer Bloch, the general linear group ''GL'' has everywhere been replaced by its Lie algebra ''gl''. 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, let  be an algebra over a field  of characteristic zero and let  be the algebra of infinite matrices over  with only finitely many nonzero entries. Then the Lie algebra homology:has a natural structure of a Hopf algebra. The space of its primitive elements of degree  is denoted by  and called the -th '''additive K-functor''' of ''A''.The additive K-functors are related to cyclic homology groups by the isomorphism:
References