In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of au...In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY239).
文摘In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.
