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A historical perspective of the theory of isotopisms. (English) Zbl 1423.17018
Summary: In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard.
Reviewer: Reviewer (Berlin)

MSC:
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
05B15 Orthogonal arrays, Latin squares, Room squares
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