Fine gradings of o(5, C), sp(4, C) and of their real forms
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Bibliographic record
Abstract
There are three fine gradings of the simple Lie algebra of type B2 over the complex number field. They provide a basic information about the structure of the algebra. In the paper an explicit description of all fine gradings is given in terms of the four-dimensional symplectic [sp(4, ℂ)] and five-dimensional orthogonal [o(5, ℂ)] representations of the algebra. In addition, the real forms of B2 are considered. It is shown which of the fine gradings survive the restriction to each of the real forms. These results should be useful in defining various sets of additive quantum numbers for systems with such symmetries, for systematic study of grading preserving contractions of this Lie algebra, and generally for choosing bases which reflect structural properties of the Lie algebra.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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