9 citations · 23 across the 11 of their papers we have counts for
11 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…
Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras
Xiangui Zhao
We mainly study the growth and Gelfand-Kirillov dimension (GK-dimension) of generalized Weyl algebra (GWA) where is a polynomial algebra or a Laurent polynomial alge…
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…
Growth of nonsymmetric operads
Zihao Qi, Yongjun Xu, James J. Zhang +1
The paper concerns the Gelfand-Kirillov dimension and the generating series of nonsymmetric operads. An analogue of Bergman's gap theorem is proved, namely, no finitely generated l…
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…
Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras
Yang Zhang, Xiangui Zhao
Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we inves…
Gelfand-Kirillov dimension of differential difference algebras
Yang Zhang, Xiangui Zhao
Differential difference algebras were introduced by Mansfield and Szanto, which arose naturally from differential difference equations. In this paper, we investigate the Gelfand-Ki…
Groebner-Shirshov bases for free inverse semigroups
L. A. Bokut, Yuqun Chen, Xiangui Zhao
A new construction of a free inverse semigroup was obtained by Poliakova and Schein in 2005. Based on their result, we find a Groebner-Shirshov basis of a free inverse semigroup re…