2021/11/26 by Vanderlei Lopes de Jesus, de Jesus, Vanderlei Lopes, Csaba Schneider +1
Mathematics · #16U70 #17B30 #17B35 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2111.13432
openalex publication_date 2021/11/26 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28
We describe the centers of the universal enveloping algebras of nilpotent Lie\nalgebras of dimension at most six over fields of prime characteristic. If the\ncharacteristic is not smaller than the nilpontency class, then the center is\nthe integral closure of the algebra generated over the p-center by the same\ngenerators that also occur in characteristic zero. Except for three examples\n(two of which are standard filiform), this algebra is already integrally closed\nand hence it coincides with the center. In the case of these three exceptional\nalgebras, the center has further generators. Then we show that the center of\nthe universal enveloping algebra of the algebras investigated in this paper is\nisomorphic to the Poisson center (the algebra of invariants under the adjoint\nrepresentation). This shows that Braun's conjecture is valid for this class of\nLie algebras.\n