English

Quantum Observables on a Completely Simple Semigroup

Rings and Algebras 2017-11-29 v1 Functional Analysis Probability Representation Theory

Abstract

Completely simple semigroups arise as the support of limiting measures of random walks on semigroups. Such a limiting measure is supported on the kernel of the semigroup. Forming tensor powers of the random walk leads to a hierarchy of the limiting kernels. Tensor squares lead to quantum observables on the kernel. Recall that zeons are bosons modulo the basis elements squaring to zero. Using zeon powers leads naturally to quantum observables which reveal the structure of the kernel. Thus asymptotic information about the random walk is related to algebraic properties of the zeon powers of the random walk.

Keywords

Cite

@article{arxiv.1711.10319,
  title  = {Quantum Observables on a Completely Simple Semigroup},
  author = {Philip Feinsilver},
  journal= {arXiv preprint arXiv:1711.10319},
  year   = {2017}
}

Comments

38 pages, two appendices. arXiv admin note: text overlap with arXiv:1103.0235

R2 v1 2026-06-22T22:59:28.501Z