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Classical affine W-algebras associated to Lie superalgebras
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Cited 7 time in Scopus
- Authors
- Issue Date
- 2016-02
- Publisher
- American Institute of Physics
- Citation
- Journal of Mathematical Physics, Vol.57 No.2, p. 021703
- Abstract
- In this paper, we prove classical affine W-algebras associated to Lie superalgebras (W-superalgebras), which can be constructed in two different ways: via affine classical Hamiltonian reductions and via taking quasi-classical limits of quantum affine W-superalgebras. Also, we show that a classical finite W-superalgebra can be obtained by a Zhu algebra of a classical affine W-superalgebra. Using the definition by Hamiltonian reductions, we find free generators of a classical W-superalgebra associated to a minimal nilpotent. Moreover, we compute generators of the classical W-algebra associated to spo(2|3) and its principal nilpotent. In the last part of this paper, we introduce a generalization of classical affine W-superalgebras called classical affine fractional W-superalgebras. We show these have Poisson vertex algebra structures and find generators of a fractional W-superalgebra associated to a minimal nilpotent. (C) 2016 AIP Publishing LLC.
- ISSN
- 0022-2488
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