Combinatorial Characters of Quasigroups

Characters of central piques

“…Following the classical extension of character theory by Frobenius, Schur et al from abelian to finite non-commutative groups, a further extension to finite quasigroups was obtained using the theories of association schemes and S-rings [6,[8][9][10][11][12][13]19]. (Note that character theory and ordinary representation theory, which are virtually indistinguishable in the usual treatments given for finite groups, diverge for finite quasigroups.…”

“…Character theory for finite quasigroups was introduced in [6][7][8][9][10][11][12][13]19] as an extension of group character theory. Within the latter theory, the character theory of abelian groups exhibits special features, generally arising from the duality theory for abelian groups that finds its fullest and most satisfactory formulation in the topological context of Pontryagin duality for locally compact abelian groups.…”

A coalgebraic approach to quasigroup permutation representations

“…One of the major programs in the study of quasigroups has been the extension to them of various aspects of the representation theory of groups. For summaries of character theory, see [7,14]. For a summary of module theory, see [13].…”

Matched pairs of $m$-invertible Hopf quasigroups

“…One of the main motivations of the theory of quasigroups may be considered to be the extension of the representation theoretical properties of the groups on the level of quasigroups; such as the character theory [26,57], module theory [56], or homogeneous spaces [58,59]. See also [21,18,22].…”