... thePoincar´e-Birkhoff-Witt theorem. Geometric Models for Noncommutative Algebras Ana Cannas da Silva1Alan Weinstein 2University of California at BerkeleyDecember 1, 19981acannas@math.berkeley.edu, ... for infinitedimensional Lie algebras, as well as for Lie algebras over arbitrary fields or rings.1.1 Universal Enveloping Algebras Regarding g just as a vector space, we may form the tensor algebra,T ... Lie algebra and theassociative algebra structures. Similarly, the Jacobi identity says that {·, w} is a derivation of the Lie algebra structure. ♦ A commutative associative algebra with a Lie algebra...