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Algebraic identities for linear operators on associative triple systems (long version)
Murray R. Bremner
We present the first classification of algebraic identities in 3 variables for linear operators on associative structures. We work in the context of associative triple systems, but…
The Veronese square of the dendriform operad
Murray R. Bremner
Veronese powers of operads were introduced in 2020 By Dotsenko, Markl, and Remm \cite{DMR}. The -th Veronese power of a weight-graded operad is the suboperad $\mat…
Operator identities of multiplicity 3 for associative algebras
Murray R. Bremner
We consider algebraic identities for linear operators on associative algebras in which each term has degree 2 (the number of variables) and multiplicity 3 (the number of occurrence…
Higher polynomial identities for mutations of associative algebras
Murray R. Bremner, Jose Brox, Juana Sánchez-Ortega
We study polynomial identities satisfied by the mutation product on the underlying vector space of an associative algebra , where are fixed elements of . W…