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4 papers · 1 filter
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…
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…
Centralizers in Free Associative Algebras and Generic Matrices
Alexei Belov-Kanel, Farrokh Razavinia, Wenchao Zhang
This paper is concerned with the completion of the proof of the Bergman centralizer theorem by using generic matrices based on our previous quantization proof \cite{KBRZh}. Additio…
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,…