Contractions and deformations of Lie algebras in Physics
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Bibliographic record
Abstract
In this contribution, we discuss the mutually opposite procedures of deformations and contractions of Lie algebras. From the group‐theoretical point of view, Einstein’s special theory of relativity is predicated on the replacement of the Galilei group by one of its deformations: the Poincaré group. Conversely, the Galilei group can be obtained by a contraction of the Poincaré group. Our principal objective is to demonstrate that appropriate combinations of both procedures may lead to new Lie algebras and thereby to new physical theories as well as new insights. To illustrate this, we recall that infinite‐dimensional Lie algebras of Krichever‐Novikov type can be retrieved by deforming the Virasoro or Kac‐Moody algebras. Then, in turn, contrations of Krichever‐Novikov algebras lead to new infinite‐dimensional Lie algebras. We end by discussing the real three‐dimensional Lie algebras. We observe that, whereas for every contraction there exists a reverse deformation, the converse is not true in general.
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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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