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Structures of (supersymmetric) classical W-algebras

Cited 3 time in Web of Science Cited 4 time in Scopus
Authors

Suh, Uhi Rinn

Issue Date
2020-11-01
Publisher
American Institute of Physics
Citation
Journal of Mathematical Physics, Vol.61 No.11, p. 111701
Abstract
In the first part of this paper, we discuss the classical W-algebra W(g,F) associated with a Lie superalgebra g and the nilpotent element F in an sl2-triple. We find a generating set of W(g,F) and compute the Poisson brackets between them. In the second part, which is the main part of this paper, we discuss supersymmetric classical W-algebras. We introduce two different constructions of a supersymmetric classical W-algebra W(g,f) associated with a Lie superalgebra g and an odd nilpotent element f in a subalgebra isomorphic to osp(1|2). The first construction is via the supersymmetric (SUSY) classical Becchi-Rouet-Stora-Tyutin (BRST) complex, and the second is via the SUSY Drinfeld-Sokolov Hamiltonian reduction. We show that these two methods give rise to isomorphic SUSY Poisson vertex algebras. As a supersymmetric analog of the first part, we compute explicit generators and Poisson brackets between the generators.
ISSN
0022-2488
URI
https://hdl.handle.net/10371/201919
DOI
https://doi.org/10.1063/5.0010006
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  • College of Natural Sciences
  • Department of Mathematical Sciences
Research Area integrable systems, vertex algebras

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