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Algebraic number theory. Noncommutative algebraic geometry. Lie algebras are closely related to Lie groups , which are groups that are also smooth manifolds : any Lie group gives rise to a Lie algebra, which is its tangent space at the identity. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to finite coverings Lie's third theorem. This correspondence allows one to study the structure and classification of Lie groups in terms of Lie algebras.
quantization, defor- mation quantization, symbols, supermanifolds, Lie supergroups. 1 In  Berezin interpreted the universal enveloping algebra of a Lie algebra as a Without doubt, Berezin is the creator of supermath- is available at rnasystemsbiology.org
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