Operads with trivial $\mathbb{A}$-actions
Yu Li, Zihao Qi, Yongjun Xu, James J. Zhang, Zerui Zhang, Xiangui Zhao

TL;DR
This paper explores operads with trivial actions, establishing an equivalence with pseudo-graded-Perm associative algebras and deriving algebraic properties such as noetherianity and centrality of elements.
Contribution
It introduces a new equivalence between $ ext{A}$-trivial operads and pseudo-graded-Perm associative algebras, revealing their algebraic structure and properties.
Findings
Finitely generated $ ext{A}$-trivial operads are right noetherian.
Such operads have integral Gelfand-Kirillov dimension.
Every element in a prime $ ext{A}$-trivial operad is central.
Abstract
We study operads with trivial -actions and prove an equivalence between the category of -trivial operads and that of pseudo-graded-Perm associative algebras. As a consequence, we show that finitely generated -trivial operads are right noetherian of integral Gelfand-Kirillov dimension and that every element in a prime -trivial operad is central.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Sphingolipid Metabolism and Signaling
