Hodge decompositions of Loday symbols inK-theory and cyclic homology Academic Article uri icon


  • In this paper, we study the Hodge decompositions of K-theory and cyclic homology induced by the operations k and k, and in particular the decomposition of the Loday symbols x, y, ... z. Except in special cases, these Loday symbols do not have pure Hodge index. In Kn(A) they can project into every component Kn(i) for 2in, and the projection of the Loday symbol x, y, ..., z into Kn(n) is a multiple of the generalized Dennis-Stein symbol x, y, ..., z. Our calculations disprove conjectures of Beilinson and Soul in K-theory, and of Gerstenhaber and Schack in Hochschild homology. 1994 Kluwer Academic Publishers.

published proceedings

  • K-Theory

author list (cited authors)

  • Geller, S. C., & Weibel, C. A.

citation count

  • 8

complete list of authors

  • Geller, Susan C||Weibel, Charles A

publication date

  • November 1994