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Leibniz Conformal Algebras of Rank Two

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Abstract

We classify all Leibniz conformal algebras of rank two.

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References

  1. D’ Andrea, A., Kac, V.: Structure theory of finite conformal algebras. Selecta Math., New Ser., 4, 377–418 (1998)

    Article  MathSciNet  Google Scholar 

  2. Bakalov, B., D’Andrea, A., Kac, V. G.: Theory of finite pseudoalgebras. Adv. Math., 162, 1–140 (2001)

    Article  MathSciNet  Google Scholar 

  3. Bakalov, B., Kac, V. G., Voronov, A. A.: Cohomology of conformal algebras. Coram. Math. Phys., 200, 561–598 (1999)

    Article  MathSciNet  Google Scholar 

  4. Belavin, A., Polyakov, A., Zamolodchikov, A.: Infinite conformal symmetry in two- dimensional quantum field theory. Nucl. Phys. B, 241, 333380 (1984)

    Article  MathSciNet  Google Scholar 

  5. Biswal, R., Chakhar, A., He, X.: Classification of rank two Lie conformal algebras, ar**v:1712.05478vl [math.RT] 15 Dec 2017

    Google Scholar 

  6. Borcherds, R.: Vertex algebras, KacMoody algebras and the Monster. Proc. Natl. Acad. Sci. USA, 83, 30683071 (1986)

    Article  Google Scholar 

  7. Cheng, S. J., Kac, V. G., Wakimoto, M.: Extensions of Conformal Modules. In Topological Field Theory, Primitive Forms and Related Topics, Progr. Math. Edited by: Kashiwara, M. and et al. Vol. 160, Boston, Birkhuser, 1998

    Google Scholar 

  8. Cheng, S., Kac, V. G.: Conformal modules. Asian J. Math., 1, 181–193 (1997)

    Article  MathSciNet  Google Scholar 

  9. Hong, Y., Li, F.: Virasoro-type Lie Conformal Algebras of rank 2. (Chinese) Chinese Ann. Math. Ser. A, 39(1), 15–32 (2018) translation in Chinese J. Contemp. Math., 39(1), 15–30 (2018)

    MathSciNet  MATH  Google Scholar 

  10. Kac, V.: Vertex algebras for beginners, volume 10 of University Lecture Series. American Mathematical Society, Providence, R1, second edition, 1998

    Google Scholar 

  11. Kac, V.: Unpublished notes at ENS, Pisa, date November 18, 1998

    Google Scholar 

  12. Retakh, A.: Unital associative pseudoalgebras and their representations. J. Algebra, 277, 769–805 (2004)

    Article  MathSciNet  Google Scholar 

  13. Sweedler, M. E.: Hopf Algebras, Math. Lecture Note Series, Benjamin, New York, 1969

    MATH  Google Scholar 

  14. Wu, Z.: Graded Left Symmetric Pseudoalgebras. Comm. Algebra, 43, 3869–3897 (2015)

    Article  MathSciNet  Google Scholar 

  15. Wu, Z.: Leibniz H-Pseudoalgebras. J. Algebra, 437, 1–33 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, P. R. China

    Zhi **ang Wu

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  1. Zhi **ang Wu
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Correspondence to Zhi **ang Wu.

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Supported by ZJNSF (Grant No. LY17A010015), and NNSFC (Grant No. 11871421)

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Wu, Z.X. Leibniz Conformal Algebras of Rank Two. Acta. Math. Sin.-English Ser. 36, 109–120 (2020). https://doi.org/10.1007/s10114-020-9057-2

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  • DOI: https://doi.org/10.1007/s10114-020-9057-2

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