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8 papers · 1 filter
Universal associative envelopes of nonassociative triple systems
Hader A. Elgendy
We construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple a…
Leibniz triple systems
Murray R. Bremner, Juana Sanchez-Ortega
We define Leibniz triple systems in a functorial manner using the algorithm of Kolesnikov and Pozhidaev which converts identities for algebras into identities for dialgebras. We ve…
Jordan Triple Disystems
Murray R. Bremner, Raul Felipe, Juana Sanchez-Ortega
We take an algorithmic and computational approach to a basic problem in abstract algebra: determining the correct generalization to dialgebras of a given variety of nonassociative…
Enveloping algebras of the nilpotent Malcev algebra of dimension five
Murray R. Bremner, Hamid Usefi
Perez-Izquierdo and Shestakov recently extended the PBW theorem to Malcev algebras. It follows from their construction that for any Malcev algebra over a field of characteristi…
Special identities for quasi-Jordan algebras
Murray R. Bremner, Luiz A. Peresi
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities , , and . These…
The partially alternating ternary sum in an associative dialgebra
Murray R Bremner, Juana Sanchez Ortega
The alternating ternary sum in an associative algebra, , gives rise to the partially alternating ternary sum in an associative dialgebra with pro…