advanced_tools:group_theory:representation_theory:adjoint_representation
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advanced_tools:group_theory:representation_theory:adjoint_representation [2020/12/26 22:49] edi [Concrete] |
advanced_tools:group_theory:representation_theory:adjoint_representation [2023/02/23 02:23] edi [Intuitive] |
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| - | The adjoint representation describes how the generators of the group, which live in the Lie algebra, transform. In other words, the adjoint representation acts on the Lie algebra. Note that the Lie algebra is a regular vector space and thus can serve as a representation space. | + | The adjoint representation describes how the generators of the group, which live in the Lie algebra, transform. In other words, the adjoint representation acts on the Lie algebra. Note that the Lie algebra is a vector space and thus can serve as a representation space. |
| The dimensionality of the adjoint representation is equal to that of the Lie algebra. For example, the adjoint representation of $SU(2)$ is 3 dimensional and the adjoint representation of $SU(3)$ is 8 dimensional. | The dimensionality of the adjoint representation is equal to that of the Lie algebra. For example, the adjoint representation of $SU(2)$ is 3 dimensional and the adjoint representation of $SU(3)$ is 8 dimensional. | ||
advanced_tools/group_theory/representation_theory/adjoint_representation.txt ยท Last modified: 2023/03/19 21:41 by edi
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