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SIGMA, 2016, Volume 12, 113, 13 pages (Mi sigma1195)  

This article is cited in 3 scientific papers (total in 3 papers)

On Free Field Realizations of $W(2,2)$-Modules

Dražen Adamovića, Gordan Radoboljab

a Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
b Faculty of Science, University of Split, Rudera Boškovića 33, 21 000 Split, Croatia

Abstract: The aim of the paper is to study modules for the twisted Heisenberg–Virasoro algebra $\mathcal H$ at level zero as modules for the $W(2,2)$-algebra by using construction from [J. Pure Appl. Algebra 219 (2015), 4322–4342, arXiv:1405.1707]. We prove that the irreducible highest weight ${\mathcal H}$-module is irreducible as $W(2,2)$-module if and only if it has a typical highest weight. Finally, we construct a screening operator acting on the Heisenberg–Virasoro vertex algebra whose kernel is exactly $W(2,2)$ vertex algebra.

Keywords: Heisenberg–Virasoro Lie algebra; vertex algebra; $W(2,2)$ algebra; screening-operators.

Funding Agency Grant Number
Croatian Science Foundation 2634
The authors are partially supported by the Croatian Science Foundation under the project 2634 and by the Croatian Scientific Centre of Excellence QuantixLie.


DOI: https://doi.org/10.3842/SIGMA.2016.113

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Full text: http://www.emis.de/journals/SIGMA/2016/113/
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Bibliographic databases:

ArXiv: 1605.08608
Document Type: Article
MSC: 17B69; 17B67; 17B68; 81R10
Received: June 9, 2016; in final form December 3, 2016; Published online December 6, 2016
Language: English

Citation: Dražen Adamović, Gordan Radobolja, “On Free Field Realizations of $W(2,2)$-Modules”, SIGMA, 12 (2016), 113, 13 pp.

Citation in format AMSBIB
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\by Dra{\v z}en~Adamovi{\'c}, Gordan~Radobolja
\paper On Free Field Realizations of $W(2,2)$-Modules
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\yr 2016
\vol 12
\papernumber 113
\totalpages 13
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Rasmussen, Ch. Raymond, “Galilean contractions of $W$ -algebras”, Nucl. Phys. B, 922 (2017), 435–479  crossref  mathscinet  zmath  isi
    2. T. Araujo, “Remarks on BMS3 invariant field theories: correlation functions and nonunitary CFTs”, Phys. Rev. D, 98:2 (2018), 026014  crossref  isi
    3. W. Jiang, Yu. Pei, W. Zhang, “Determinant formula and a realization for the Lie algebra $W(2,2)$”, Sci. China-Math., 61:4 (2018), 685–694  crossref  mathscinet  zmath  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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