Information AboutCoroot |
| CATEGORIES ABOUT COROOT | |
| lie algebras | |
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In Mathematics , a coroot is a certain kind of element of Cartan Subalgebra of a complex Semisimple Lie Algebra ''g''. The structure and representation theory of ''g'' is characterised by its Root System . Given a root, α of a ''g'', there are associated to it two Operator s; : and : known as the raising and lowering operators respectively. Their Lie bracket, : is an element of the Cartan subalgebra. These raising and lowering operators are determined only up to scalar multipliers. It is often useful to set their lengths so as to form a subalgebra isomorphic to sl the Lie algebra of the Special Linear Group , of dimension 3. Once this has been done : is the ''coroot'' associated to α (French ''copoid''). |
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