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.
Keywords: quasigroup, ternary quasigroup, $n$-quasigroup, heterogeneous algebra, hyperidentity, modular group, conjugate, parastrophe, time reversal
AMS Subject Classification: Primary 20N05; Secondary 08A68