English

No-go theorems for functorial localic spectra of noncommutative rings

Rings and Algebras 2012-10-03 v3 Category Theory Quantum Physics

Abstract

Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in categories other than that of locales is briefly discussed.

Keywords

Cite

@article{arxiv.1101.5924,
  title  = {No-go theorems for functorial localic spectra of noncommutative rings},
  author = {Benno van den Berg and Chris Heunen},
  journal= {arXiv preprint arXiv:1101.5924},
  year   = {2012}
}

Comments

In Proceedings QPL 2011, arXiv:1210.0298