Contractions of affine Kac-Moody algebras

J. Daboul; C. Daboul; M. De Montigny

doi:10.1088/1742-6596/128/1/012054

Contractions of affine Kac-Moody algebras

J. Daboul, C. Daboul, M. De Montigny

Department of Physics

Research output: Contribution to journal › Article › peer-review

Abstract

I review our recent work on contractions of affine Kac-Moody algebras (KMA) and present new results. We study generalized contractions of KMA with respect to their twisted and untwisted KM subalgebras. As a concrete example, we discuss contraction of D⁽¹⁾₄ and D⁽³⁾₄, based on Z₃-grading. We also describe examples of "level-dependent" contractions, which are based on Z-gradings of KMA. Our work generalizes the Inönü-Wigner contraction of P. Majumdar in several directions. We also give an algorithm for constructing Kac-Moody-like algebras for any Lie algebra g.

Original language	English
Article number	012054
Journal	Journal of Physics: Conference Series
Volume	128
DOIs	https://doi.org/10.1088/1742-6596/128/1/012054
State	Published - 1 Jan 2008

ASJC Scopus subject areas

General Physics and Astronomy

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10.1088/1742-6596/128/1/012054

Cite this

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abstract = "I review our recent work on contractions of affine Kac-Moody algebras (KMA) and present new results. We study generalized contractions of KMA with respect to their twisted and untwisted KM subalgebras. As a concrete example, we discuss contraction of D(1)4 and D(3)4, based on Z3-grading. We also describe examples of {"}level-dependent{"} contractions, which are based on Z-gradings of KMA. Our work generalizes the In{\"o}n{\"u}-Wigner contraction of P. Majumdar in several directions. We also give an algorithm for constructing Kac-Moody-like algebras for any Lie algebra g.",

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AB - I review our recent work on contractions of affine Kac-Moody algebras (KMA) and present new results. We study generalized contractions of KMA with respect to their twisted and untwisted KM subalgebras. As a concrete example, we discuss contraction of D(1)4 and D(3)4, based on Z3-grading. We also describe examples of "level-dependent" contractions, which are based on Z-gradings of KMA. Our work generalizes the Inönü-Wigner contraction of P. Majumdar in several directions. We also give an algorithm for constructing Kac-Moody-like algebras for any Lie algebra g.

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Contractions of affine Kac-Moody algebras

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