2025/12/12 by Bremner, Murray R.
Mathematics · #17A30 #17A50 #17B38 #18M65 #68W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 17A40. Secondary 17-08 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.11703
openalex publication_date 2025/12/12 · openalex created_date 2025/12/16 · openalex updated_date 2026/07/28
Veronese powers of operads were introduced in 2020 By Dotsenko, Markl, and Remm \citeDMR. The m-th Veronese power of a weight-graded operad V is the suboperad V[m] generated by the operations of weight m. If V is generated by binary operations and governs the variety V of algebras, this gives a natural definition of the concept of (m+1)-ary V-algebras. In particular, the Veronese square (m=2) corresponds to ternary algebras. We choose five generating operations for the Veronese square of the dendriform operad. We represent the dendriform operad as a suboperad of the Rota-Baxter operad, and express the quadratic relations satisfied by the generating operations as the kernel of a rewriting map. We use combinatorics of monomials and computational linear algebra to determine the kernel. We obtain 33 linearly independent quadratic relations satisfied by the Veronese square.