Definition: Birkhoff, in mathematics, a member of a family of non-abelian groups associated with Lie algebras, first introduced in 1920 to generalize the notion of "Lie group" to include non-compact Lie algebras. His contributions included:
1.
Definition
: A group is said to be `Birkhoff algebraic` if it admits a unique finite-dimensional representation that is a subalgebra of the universal enveloping algebra, and the map from this finite-dimensional representation to its center is an automorphism.
2.
Applications
: Birkhoff's work has found applications in non-commutative geometry, quantum groups, Lie theory, and group representations.
Definition
:
A group (G) is said to be `Birkhoff algebraic` if it admits a unique finite-dimensional representation that is a subalgebra of the universal enveloping algebra, and the map from this finite-dimensional representation to its center is an automorphism. The group (G) can be interpreted as having an underlying topological space.
Applications
: Birkhoff's work has found applications in non-commutative geometry, quantum groups, Lie theory, and group representations.
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