PBWfor an inclusion of Lie algebras

摘要: Abstract Let h ⊂ g be an inclusion of Lie algebras with quotient -module n . There is a natural degree filtration on the U ( ) / whose associated graded isomorphic to S We give necessary and sufficient condition for existence splitting this filtration. In turn such yields isomorphism between -modules For diagonal embedding ⊕ automatically satisfied we recover classical Poincare–Birkhoff–Witt theorem. The main theorem its proof are direct translations results in algebraic geometry, obtained using ad hoc dictionary. This suggests unified framework allowing simultaneous study varieties, closely related work direction way.