Delta methods in enveloping rings
Let L be a Lie algebra over a field K of characteristic 0 with a universal enveloping algebra U(L) (or a restricted Lie algebra with restricted enveloping algebra u(L) when char K\(=p>0)\) and let L act on a K-algebra R as K-derivations. The authors consider the twisted smash products R{\#}U(L) and R{\#}u(L). The main purpose of the paper is to reduce questions about these rings to analogous ones for R{\#}U(\(\Delta\)) and R{\#}u(\(\Delta\)), where \(\Delta (L)=\{x\in L|\dim_ KL/C_ L(x)<\infty \}\) is the Lie algebra analog of the finite conjugate centre of a group. The authors establish results on annihilator ideals and primeness of R{\#}U(L) and R{\#}u(L), and on X-inner automorphisms and derivations, intersection theorems and primitivity of the twisted enveloping algebras of L.
scientific article; zbMATH DE number 4181561
scientific article