| Title:
|
A class of quasigroups solving a problem of ergodic theory (English) |
| Author:
|
Smith, Jonathan D. H. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
409-414 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
quasigroup |
| Keyword:
|
Latin square |
| Keyword:
|
Markov chain |
| Keyword:
|
doubly stochastic matrix |
| Keyword:
|
ergodic |
| Keyword:
|
superergodic |
| Keyword:
|
dripping faucet |
| Keyword:
|
group isotope |
| Keyword:
|
central quasigroup |
| Keyword:
|
semicentral quasigroup |
| Keyword:
|
$T$-quasigroup |
| Keyword:
|
left linear quasigroup |
| MSC:
|
20N05 |
| MSC:
|
60J10 |
| idZBL:
|
Zbl 1038.20054 |
| idMR:
|
MR1780882 |
| . |
| Date available:
|
2009-01-08T19:02:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119174 |
| . |
| Reference:
|
Ash R.B.: Information Theory.Wiley New York, NY (1965). Zbl 0141.34904, MR 0229475 |
| Reference:
|
Belyavskaja G.B., Tabarov A.H.: The nuclei and center of linear quasigroups (in Russian).Izv. Akad. Nauk Respub. Moldova Mat. 3 (1991), 37-42. MR 1174875 |
| Reference:
|
Belyavskaja G.B., Tabarov A.H.: One-sided T-quasigroups and irreducible balanced identities.Quasigroups Related Systems 1 (1994), 8-21. MR 1327942 |
| Reference:
|
Chein O., Pflugfelder H.O., Smith J.D.H. (eds.): Quasigroups and Loops: Theory and Applications.Heldermann Berlin (1990). Zbl 0719.20036, MR 1125806 |
| Reference:
|
Feller W.: An Introduction to Probability Theory and its Applications, Volume I.Wiley New York, NY (1950). MR 0038583 |
| Reference:
|
Horibe Y.: On the increase of conditional entropy in Markov chains.in ``Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Volume A'', Academia, Prague, 1988, pp.391-396. Zbl 0707.60059, MR 1136296 |
| Reference:
|
Ježek J., Kepka T.: Quasigroups, isotopic to a group.Comment. Math. Univ. Carolinae 16 (1975), 59-76. MR 0367103 |
| Reference:
|
Němec P., Kepka T.: T-quasigroups I, II.Acta Univ. Carolinae - Math. et Phys. 12 (1971), 1 39-49 and no. 2, 31-49. MR 0320206 |
| Reference:
|
Smith J.D.H.: Mal'cev Varieties.Springer Berlin (1976). Zbl 0344.08002, MR 0432511 |
| Reference:
|
Smith J.D.H., Romanowska A.B.: Post-Modern Algebra.Wiley New York, NY (1999). Zbl 0946.00001, MR 1673047 |
| . |
