A local-global principle for linear dependence in enveloping algebras of Lie algebras

摘要

For an associative algebra A and a class C of representations of A the following question (related to nullstellensatz) makes sense: Characterize all tuples of elements a(1 ),..., a(n) is an element of A such that vectors pi(a(1))upsilon ,..., pi(a(n))upsilon are linearly dependent for every pi is an element of A and every upsilon in the representation space of pi. We answer this question in the following cases: