English

On the Toeplitz-Jacobson algebra and direct finiteness

Rings and Algebras 2016-03-02 v1 Representation Theory

Abstract

We study the representation theory of the algebraic Toeplitz algebra R=Kx,y/xy1R={\mathbb K}\langle x,y\rangle/\langle xy-1\rangle, give a few new structure and homological theorems, completely determine one-sided ideals and survey and re-obtain results from the existing literature as well. We discuss its connection to Kaplansky's direct finiteness conjecture, and a possible approach to it based on the module theory of RR. In addition, we discuss the conjecture's connections to several central problems in mathematics, including Connes' embedding conjecture.

Keywords

Cite

@article{arxiv.1603.00109,
  title  = {On the Toeplitz-Jacobson algebra and direct finiteness},
  author = {Miodrag C Iovanov and Alexander Sistko},
  journal= {arXiv preprint arXiv:1603.00109},
  year   = {2016}
}
R2 v1 2026-06-22T13:00:33.364Z