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Sets with two associative operations. (English) Zbl 1032.16032
The author considers sets equipped with two associative binary operations, calling such a structure a duplex. Relevant examples of duplexes are dimonoids, defined by J.-L. Loday [C. R. Acad. Sci., Paris, Sér. I 321, No. 2, 141-146 (1995; Zbl 0845.16036)]. An example of a duplex which is not a dimonoid is given by using permutations. A free duplex generated by a given set is constructed via planar trees. Duplexes coming from planar binary trees and vertices of cubes are discussed.

MSC:
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17A32 Leibniz algebras
20M05 Free semigroups, generators and relations, word problems
08B20 Free algebras
05C05 Trees
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References:
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