3 papers
math.RA2023
Gröbner-Shirshov bases and linear bases for free multi-operated algebras over algebras with applications to differential Rota-Baxter algebras and integro-differential algebras
Zuan Liu, Zihao Qi, Yufei Qin +1
Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An -operated…
math.RA2022
-structures and cohomology theory of compatible -operators and compatible dendriform algebras
Apurba Das, Shuangjian Guo, Yufei Qin
The notion of -operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible -operator…
math.RA2021
Gröbner-Shirshov bases and linear bases for free differential type algebras over algebras
Zihao Qi, Yufei Qin, Guodong Zhou
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra together with a Gröbner-Shirshov basis , consider the free operated algebra…