An Introduction to Quasigroups and Their Representations

An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups. The book first presents the fundamentals of quasigroup and loop theory, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters focus on the three main branches of representation theory: permutation representations of quasigroups, combinatorial character theory, and quasigroup module theory. Each chapter includes exercises and examples to demonstrate how the theories discussed relate to practical applications. The book concludes with appendices that summarize some essential topics from category theory, universal algebra, and coalgebras.