On the Toeplitz-Jacobson algebra and direct finiteness

Miodrag C Iovanov; Alexander Sistko

doi:10.48550/arXiv.1603.00109

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On the Toeplitz-Jacobson algebra and direct finiteness

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On the Toeplitz-Jacobson algebra and direct finiteness

Miodrag C Iovanov and Alexander Sistko

ArXiv.org

02/29/2016

DOI: 10.48550/arXiv.1603.00109

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Abstract

We study the representation theory of the algebraic Toeplitz algebra R=K⟨x,y⟩/⟨xy−1⟩, 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 R. In addition, we discuss the conjecture's connections to several central problems in mathematics, including Connes' embedding conjecture.

Details

Title: Subtitle: On the Toeplitz-Jacobson algebra and direct finiteness
Creators: Miodrag C Iovanov
Alexander Sistko
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.1603.00109
ISSN: 2331-8422
Language: English
Date posted: 02/29/2016
Academic Unit: Mathematics
Record Identifier: 9984240865502771

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