Poletaeva, E. Superconformal algebras and Lie superalgebras of the Hodge theory. (English) Zbl 1044.17017 J. Nonlinear Math. Phys. 10, No. 2, 141-147 (2003). The author discusses certain isomorphisms between Lie superalgebras that show up in two different fields: on the one hand, certain Lie superalgebras generated by the operators of Hodge theory for Kähler and hyper-Kähler manifolds, and on the other hand, Lie superalgebras related to superconformal algebras considered in the paper by V. G. Kac and J. W. van de Leur [in: Strings’88. Proceedings of a workshop, May 24–28, 1988 at University of Maryland, at College Park, Baltimore, MD, USA (World Scientific, Singapore) 77–106 (1989; Zbl 0938.17500)]. Reviewer: Daniel Beltiţă (Bucureşti) Cited in 4 Documents MSC: 17B68 Virasoro and related algebras 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Lie superalgebra; Hodge theory Citations:Zbl 0938.17500 PDFBibTeX XMLCite \textit{E. Poletaeva}, J. Nonlinear Math. Phys. 10, No. 2, 141--147 (2003; Zbl 1044.17017) Full Text: DOI arXiv References: [1] Feigin B, Commun. Math. Phys. 137 pp 617– (1991) · Zbl 0726.17035 [2] Figueroa-O’Farrill J M, Nucl. Phys. 503 pp 614– (1997) · Zbl 0938.81041 [3] Frenkel I B, Proc. Nat. Acad. Sci. USA 83 pp 8442– (1986) · Zbl 0607.17007 [4] Green M Schwarz J Witten E Superstring Theory, Vol. 1, 2, Second edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1988 [5] Griffiths P Harris J Principles of Algebraic Geometry, Wiley-Interscience Publ., New York, 1978 [6] Grozman P, Acta Math. Vietnam. 26 pp 27– (2001) [7] Howe R, Trans. Amer. Math. Soc. 313 pp 539– (1989) [8] Kac V G van de Leur J W On Classification of Superconformal Algebras, in Strings-88, Editors Gates S J et al., World Scientific Publ., Teaneck, NJ, 1989, 77–106 · Zbl 0938.17500 [9] Kac V G, Commun. Math. Phys. 186 pp 233– (1997) · Zbl 0886.17021 [10] Poletaeva E, Ann. Inst. Fourier 51 pp 745– (2001) · Zbl 1067.17012 [11] Verbitsky M, Funct. Anal. Appl. 24 pp 70– (1990) · Zbl 0714.47022 [12] Verbitsky M, J. Algebraic Geom. 5 pp 633– (1996) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.