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Classical affine W-algebras associated to Lie superalgebras

Cited 7 time in Web of Science Cited 7 time in Scopus
Authors

Suh, Uhi Rinn

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
URI
https://hdl.handle.net/10371/201924
DOI
https://doi.org/10.1063/1.4940879
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  • College of Natural Sciences
  • Department of Mathematical Sciences
Research Area integrable systems, vertex algebras

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