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Lie Groups, Physics, and Geometry by Robert Gilmore

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6

Operator algebras

 

 

Lie algebras of matrices can be mapped onto Lie algebras of operators in a number of different ways. Three useful matrix algebra to operator algebra mappings are described in this chapter.

6.1 Boson operator algebras

It is possible to construct useful operator algebras from Lie algebras. An operator Lie algebra can be constructed from a Lie algebra of n × n matrices by introducing a set of n independent boson creation (bi) and annihilation (bj) operators that obey the commutation relations

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