{
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      "year": "2023"
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  "authors": [
    {
      "surname": "Drachov", 
      "given_names": "Ya.", 
      "affiliations": [
        {
          "country": "Russia", 
          "value": "MIPT, Dolgoprudny, Russia"
        }
      ], 
      "full_name": "Drachov, Ya.", 
      "orcid": "0000-0001-9112-7792", 
      "email": "drachov.yai@phystech.edu"
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    {
      "surname": "Mironov", 
      "given_names": "A.", 
      "affiliations": [
        {
          "country": "Russia", 
          "value": "Lebedev Physics Institute, Moscow, Russia"
        }, 
        {
          "country": "Russia", 
          "value": "NRC \u201cKurchatov Institute\u201d, Moscow, Russia"
        }, 
        {
          "country": "Russia", 
          "value": "Institute for Information Transmission Problems, Moscow, Russia"
        }
      ], 
      "full_name": "Mironov, A.", 
      "orcid": "0000-0001-9598-7968", 
      "email": "mironov@lpi.ru"
    }, 
    {
      "affiliations": [
        {
          "country": "Russia", 
          "value": "MIPT, Dolgoprudny, Russia"
        }, 
        {
          "country": "Russia", 
          "value": "NRC \u201cKurchatov Institute\u201d, Moscow, Russia"
        }, 
        {
          "country": "Russia", 
          "value": "Institute for Information Transmission Problems, Moscow, Russia"
        }
      ], 
      "surname": "Popolitov", 
      "email": "popolit@gmail.com", 
      "full_name": "Popolitov, A.", 
      "given_names": "A."
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  "titles": [
    {
      "source": "Elsevier", 
      "title": "And algebras, and Ward identities"
    }
  ], 
  "collections": [
    {
      "primary": "Physics Letters B"
    }
  ], 
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    {
      "value": "10.1016/j.physletb.2023.138426"
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  "publication_info": [
    {
      "journal_volume": "849 C", 
      "journal_title": "Physics Letters B", 
      "material": "article", 
      "artid": "138426", 
      "year": 2023
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "abstracts": [
    {
      "source": "Elsevier", 
      "value": "It was demonstrated recently that the <math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>+</mo><mo>\u221e</mo></mrow></msub></math> algebra contains commutative subalgebras associated with all integer slope rays (including the vertical one). In this paper, we realize that every element of such a ray is associated with a generalized <math><mover><mrow><mi>W</mi></mrow><mrow><mo>\u02dc</mo></mrow></mover></math> algebra. In particular, the simplest commutative subalgebra associated with the rational Calogero Hamiltonians is associated with the <math><mover><mrow><mi>W</mi></mrow><mrow><mo>\u02dc</mo></mrow></mover></math> algebras studied earlier. We suggest a definition of the generalized <math><mover><mrow><mi>W</mi></mrow><mrow><mo>\u02dc</mo></mrow></mover></math> algebra as differential operators in variables <math><msub><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msub></math> basing on the matrix realization of the <math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>+</mo><mo>\u221e</mo></mrow></msub></math> algebra, and also suggest an unambiguous recursive definition, which, however, involves more elements of the <math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>+</mo><mo>\u221e</mo></mrow></msub></math> algebra than is contained in its commutative subalgebras. The positive integer rays are associated with <math><mover><mrow><mi>W</mi></mrow><mrow><mo>\u02dc</mo></mrow></mover></math> algebras that form sets of Ward identities for the WLZZ matrix models, while the vertical ray associated with the trigonometric Calogero-Sutherland model describes the hypergeometric \u03c4-functions corresponding to the completed cycles."
    }
  ], 
  "imprints": [
    {
      "date": "2023-12-29", 
      "publisher": "Elsevier"
    }
  ], 
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    "source": "Elsevier", 
    "method": "Elsevier", 
    "submission_number": "6323940602e611ef81c58e7301cc4a06"
  }
}