English

Noncommutative cross-ratio and Schwarz derivative

Rings and Algebras 2019-05-23 v3

Abstract

We present here a theory of noncommutative cross-ratio, Schwarz derivative and their connections and relations to the operator cross-ratio. We apply the theory to "noncommutative elementary geometry" and relate it to noncommutative integrable systems. We also provide a noncommutative version of the celebrated "pentagramma mirificum".

Keywords

Cite

@article{arxiv.1905.01366,
  title  = {Noncommutative cross-ratio and Schwarz derivative},
  author = {Vladimir Retakh and Vladimir Rubtsov and Georgy Sharygin},
  journal= {arXiv preprint arXiv:1905.01366},
  year   = {2019}
}

Comments

24 pages, 3 figures. We add in the v.2 one figure and few references. We also had made some cosmetic language and phrase order changes

R2 v1 2026-06-23T08:56:43.365Z