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| Property | SU(2) | SO(3) |
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| Category | Compact real Lie group | Compact real Lie group |
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| Order | Not applicable: positive-dimensional Lie group | Not applicable: positive-dimensional Lie group |
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| Real dimension | 3 | 3 |
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| Center | ℤ₂ | Trivial |
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| Fundamental group | 0 | ℤ₂ |
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| Representation data | Highest weight n = 2j ≥ 0; dimension n + 1. Even n has real type, odd n quaternionic type. | Ordinary irreducible complex representations have integer spin j. Half-integer-spin representations belong to the spin cover. |
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| Reality types | See the representation category and stated scope | See the representation category and stated scope |
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| Coverage | executable | executable |
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| Supported tools | global-forms, tensor-products, branching, topology, lie-representations, matter-quotients, sun-tensor-products | global-forms, topology |
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Shaded rows differ. Unavailable and inapplicable data are labeled separately. Open either record for sources.