2019/04/17 by Pak-Hin Li, Li, Pak-Hin
Mathematics · #16S30 #17B08 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1904.08470
openalex publication_date 2019/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Q be a finite type quiver i.e. ADE Dynkin quiver. Denote by Λ its preprojective algebra. It is known that there are finitely many indecomposable Λ-modules if and only if Q is of type A1,A2,A3,A4. In this paper, extending Lusztig's construction of U\frakn+, we study an algebra generated by these indecomposable submodules. It turns out that it forms the universal enveloping algebra of some nilpotent Lie algebra inside the function algebra on Lusztig's nilpotent scheme. The defining relations of the corresponding nilpotent Lie algebra for type A1, A2,A3,A4 are given here.