Hochschild homology and global dimension

Abstract

We prove that for certain classes of graded algebras (Koszul, local, cellular), infinite global dimension implies that Hochschild homology does not vanish in high degrees, provided the characteristic of the ground field is zero. Our proof uses Igusa's formula relating the Euler characteristic of relative cyclic homology to the graded Cartan determinant.

11 pages

Cited by in corpus (7)

• Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
• Split bounded extension algebras and Han's conjecture
• Han's conjecture and Hochschild homology for null-square projective algebras
• Han's conjecture for bounded extensions
• Two classes of algebras with infinite Hochschild homology
• Hochschild homology and trivial extensions
• Hochschild homology, global dimension, and truncated oriented cycles