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Article

Smith, Jonathan D. H.
A class of quasigroups solving a problem of ergodic theory. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 41 (2000), issue 2, pp. 409-414
MSC: 20N05, 60J10 | MR 1780882 | Zbl 1038.20054
Keywords:
quasigroup; Latin square; Markov chain; doubly stochastic matrix; ergodic; superergodic; dripping faucet; group isotope; central quasigroup; semicentral quasigroup; $T$-quasigroup; left linear quasigroup
Summary:
A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.
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