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- In mathematics, the special linear Lie algebra of order n (denoted or ) is the Lie algebra of matrices with trace zero and with the Lie bracket . This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. (en)
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- 10458 (xsd:nonNegativeInteger)
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- Let be a representation of that may have infinite dimension and a vector in that is a -weight vector . Then
*Those 's that are nonzero are linearly independent.
*If some is zero, then the -eigenvalue of v is a nonnegative integer such that are nonzero and . Moreover, the subspace spanned by the 's is an irreducible -subrepresentation of . (en)
- Let be a representation of and a vector in it. Set for each . If is an eigenvector of the action of ; i.e., for some complex number , then, for each ,
*.
*.
*. (en)
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- In mathematics, the special linear Lie algebra of order n (denoted or ) is the Lie algebra of matrices with trace zero and with the Lie bracket . This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. (en)
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- Special linear Lie algebra (en)
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