Split Lie algebra (original) (raw)
리 대수 이론에서, 분할 리 대수(分割Lie代數, 영어: split Lie algebra)는 특별한 형태의 카르탕 부분 대수를 갖춘 리 대수이다. 복소수체 위의 반단순 리 대수는 항상 분할 리 대수의 구조를 갖는다.
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| dbo:abstract | In the mathematical field of Lie theory, a split Lie algebra is a pair where is a Lie algebra and is a splitting Cartan subalgebra, where "splitting" means that for all , is triangularizable. If a Lie algebra admits a splitting, it is called a splittable Lie algebra. Note that for reductive Lie algebras, the Cartan subalgebra is required to contain the center. Over an algebraically closed field such as the complex numbers, all semisimple Lie algebras are splittable (indeed, not only does the Cartan subalgebra act by triangularizable matrices, but even stronger, it acts by diagonalizable ones) and all splittings are conjugate; thus split Lie algebras are of most interest for non-algebraically closed fields. Split Lie algebras are of interest both because they formalize the split real form of a complex Lie algebra, and because split semisimple Lie algebras (more generally, split reductive Lie algebras) over any field share many properties with semisimple Lie algebras over algebraically closed fields – having essentially the same representation theory, for instance – the splitting Cartan subalgebra playing the same role as the Cartan subalgebra plays over algebraically closed fields. This is the approach followed in, for instance. (en) 리 대수 이론에서, 분할 리 대수(分割Lie代數, 영어: split Lie algebra)는 특별한 형태의 카르탕 부분 대수를 갖춘 리 대수이다. 복소수체 위의 반단순 리 대수는 항상 분할 리 대수의 구조를 갖는다. (ko) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=l8nJCNiIQAAC&pg=PA157 https://books.google.com/books%3Fid=Yh1RHnYCDNsC&pg=PA69 |
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| rdfs:comment | 리 대수 이론에서, 분할 리 대수(分割Lie代數, 영어: split Lie algebra)는 특별한 형태의 카르탕 부분 대수를 갖춘 리 대수이다. 복소수체 위의 반단순 리 대수는 항상 분할 리 대수의 구조를 갖는다. (ko) In the mathematical field of Lie theory, a split Lie algebra is a pair where is a Lie algebra and is a splitting Cartan subalgebra, where "splitting" means that for all , is triangularizable. If a Lie algebra admits a splitting, it is called a splittable Lie algebra. Note that for reductive Lie algebras, the Cartan subalgebra is required to contain the center. (en) |
| rdfs:label | 분할 리 대수 (ko) Split Lie algebra (en) |
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