2 citations · 2 across the 4 of their papers we have counts for
5 papers
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…
Growth of associated monomial algebras with application to Manturov groups
Xiangui Zhao
It is well-known that an associative algebra shares the same growth and Gelfand-Kirillov dimension (GK-dimension) as its associated monomial algebra with respect to a degree-lexico…
Cancellation of Morita and Skew Types
Xin Tang, James J. Zhang, Xiangui Zhao
We study both Morita cancellative and skew cancellative properties of noncommutative algebras as initiated recently in several papers and explore that which classes of noncommutati…
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…