We study operads with trivial ๐ธ-actions and prove an equivalence between the category of ๐ธ-trivial operads and that of pseudo-graded-Perm associative algebras. As a consequence, we show that finitely generated ๐ธ-trivial operads are right noetherian of integral Gelfand-Kirillov dimension and that every element in a prime ๐ธ-trivial operad is central.
Li et al. (Fri,) studied this question.
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