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.
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