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Steinberg unitary Lie conformal algebras

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In this paper, we study Steinberg unitary Lie conformal algebras, which are universal central extensions of unitary Lie conformal algebras. We describe the kernels of these extensions by means of skew-dihedral homology.

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References

  1. B. N. Allison and J. R. Faulkner, “Nonassociative coefficient algebras for Steinberg unitary Lie algebras,” J. Algebra, 161, 1–19 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  2. L. A. Bokut, Y. Fong, and W.-F. Ke, “Gröbner-Shirshov bases and composition lemma for associative conformal algebras: An example,” Contemp. Math., 264, 63–90 (2000).

    MathSciNet  Google Scholar 

  3. J. B. Humphreys, Introduction to Lie Algebras and Representation Theory, Cambridge Univ. Press, Cambridge (1990).

    Google Scholar 

  4. V. Kac, Vertex Algebras for Beginners, University Lecture Series, Vol. 10, AMS, Providence, RI (1996)

    MATH  Google Scholar 

  5. C. Kasser, “Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra,” J. Pure Appl. Algebra, 34, 265–275 (1984).

    Article  MathSciNet  Google Scholar 

  6. C. Kasser and J. L. Loday, “Extensions centrales d’algèbres de Lie,” Ann. Inst. Fourier, 32, 119–142 (1982).

    Google Scholar 

  7. A. V. Mikhalev and I. A. Pinchuk, “Steinberg conformal algebras,” Mat. Sb., 196, No. 5, 31–52 (2005).

    MathSciNet  Google Scholar 

  8. A. V. Mikhalev and I. A. Pinchuk, “Universal central extensions of Lie conformal algebras,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 1, 26–31 (2005).

  9. Yun Gao, “Steinberg Lie algebras and skew-dihedral homology,” J. Algebra, 179, 261–304 (1996).

    Article  MATH  MathSciNet  Google Scholar 

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 135–155, 2005.

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Mikhalev, A.V., Pinchuk, I.A. Steinberg unitary Lie conformal algebras. J Math Sci 142, 1954–1968 (2007). https://doi.org/10.1007/s10958-007-0103-8

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  • DOI: https://doi.org/10.1007/s10958-007-0103-8

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