Ternary quasigroups and the modular group

@article{Smith2008,
abstract = {For a positive integer $n$, the usual definitions of $n$-quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin $n$-cubes, or by $2n$ identities on $n+1$ different $n$-ary operations. In this paper, a more symmetrical approach to the specification of $n$-quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.},
author = {Smith, Jonathan D. H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroup; ternary quasigroup; $n$-quasigroup; heterogeneous algebra; hyperidentity; modular group; conjugate; parastrophe; time reversal; quasigroups; -quasigroups; modular group; conjugates; -ary quasigroups; hyperquasigroups; identities},
language = {eng},
number = {2},
pages = {309-317},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Ternary quasigroups and the modular group},
url = {http://eudml.org/doc/250486},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Smith, Jonathan D. H.
TI - Ternary quasigroups and the modular group
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 309
EP - 317
AB - For a positive integer $n$, the usual definitions of $n$-quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin $n$-cubes, or by $2n$ identities on $n+1$ different $n$-ary operations. In this paper, a more symmetrical approach to the specification of $n$-quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.
LA - eng
KW - quasigroup; ternary quasigroup; $n$-quasigroup; heterogeneous algebra; hyperidentity; modular group; conjugate; parastrophe; time reversal; quasigroups; -quasigroups; modular group; conjugates; -ary quasigroups; hyperquasigroups; identities
UR - http://eudml.org/doc/250486
ER -