A Survey on Han's Conjecture
K-Theory and Homology
2023-09-18 v2 Category Theory
Rings and Algebras
Representation Theory
Abstract
In 1989, D. Happel pointed out for a possible connection between the global dimension of a finite-dimensional algebra and its Hochschild cohomology: is it true that the vanishing of Hochschild cohomology higher groups is sufficient to deduce that the global dimension is finite? After the discovery of a counterexample, Y. Han proposed, in 2006, to reformulate this question to homology. In this survey, after introducing the concepts and results involved, I present the efforts made until now towards the comprehension of Han's conjecture; which includes: examples of algebras that have been proven to satisfy it and extensions that preserve it.
Cite
@article{arxiv.2301.07511,
title = {A Survey on Han's Conjecture},
author = {Guilherme da Costa Cruz},
journal= {arXiv preprint arXiv:2301.07511},
year = {2023}
}