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The universal enveloping algebra is a fundamental concept in the theory of Lie algebras and representation theory. Given a Lie algebra \(\mathfrak{g}\), its universal enveloping algebra, denoted as \(U(\mathfrak{g})\), is an associative algebra that encodes the structure of the Lie algebra in such a way that representation theory can be applied to it using methods of associative algebras.

Ancestors (6)

  1. Representation theory of Lie algebras
  2. Representation theory
  3. Fields of abstract algebra
  4. Fields of mathematics
  5. Mathematics
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