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math.RA2026
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…
math.RA2025
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…
math.RA2025
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…