15 citations · 42 across the 11 of their papers we have counts for
10 papers · 1 filter
Symmetric operads of GK-dimension one
Yu Li, Zihao Qi, Yongjun Xu +3
We prove that there is no finitely generated symmetric operad of Gelfand-Kirillov dimension strictly between 1 and 2 that answers an open question posted in 2020. We also classify…
Operads with trivial -actions
Yu Li, Zihao Qi, Yongjun Xu +3
We study operads with trivial -actions and prove an equivalence between the category of -trivial operads and that of pseudo-graded-Perm associative algebras…
The Freiheitssatz and automorphisms for free brace algebras
Yu Li, Qiuhui Mo, Xiangui Zhao
Over a field of characteristic zero, we prove that the Freiheitssatz holds for brace algebras, the word problem for the brace algebras with a single defining relation is decidable,…
Groebner-Shirshov bases for brace algebras
Yu Li, Qiuhui Mo, Xiangui Zhao
Let be a brace algebra. This structure implies that is also a pre-Lie algebra. In this paper, we establish Composition-Diamond lemma for brace algebras. Using this Composit…
Lyndon-Shirshov basis and anti-commutative algebras
L. A. Bokut, Yuqun Chen, Yu Li
Chen, Fox, Lyndon 1958 \cite{CFL58} and Shirshov 1958 \cite{Sh58} introduced non-associative Lyndon-Shirshov words and proved that they form a linear basis of a free Lie algebra, i…
Gröbner-Shirshov bases for categories
L. A. Bokut, Yuqun Chen, Yu Li
In this paper we establish Composition-Diamond lemma for small categories. We give Gröbner-Shirshov bases for simplicial category and cyclic category.
Gröbner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras
L. A. Bokut, Yuqun Chen, Yu Li
In this paper, we establish the Composition-Diamond lemma for right-symmetric algebras. As an application, we give a Gröbner-Shirshov basis for universal enveloping right--symmetri…
Composition-Diamond lemma for differential algebras
Yuqun Chen, Yongshan Chen, Yu Li
In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Groebner-Shirshov bases for free Lie-differential algebra and fre…
Anti-commutative Groebner-Shirshov basis of a free Lie algebra
L. A. Bokut, Yuqun Chen, Yu Li
One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by…
Some remarks for the Akivis algebras and the Pre-Lie algebras
Yuqun Chen, Yu Li
In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and…