Abstract
We will present a survey on infinite dimensional graded Lie and Jordan superalgebras and their representations.
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References
C. Boyallian, V.G. Kac, J.I. Liberati, A. Rudakov, Representations of simple finite Lie conformal superalgebras of type W and S. J. Math. Phys. 47, 043513 (2006)
C. Boyallian, V.G. Kac, J.I. Liberati, Irreducible modules over finite simple Lie conformal superalgebras of type K. J. Math. Phys. 51, 063507 (2010)
C. Boyallian, V.G. Kac, J.I. Liberati, Classification of finite irreducible modules over the Lie conformal superalgebra CK 6. Commun. Math. Phys. 317 (2), 503–546 (2013)
N. Cantarini, V. Kac, Classification of linearly compact simple Jordan and generalized Poisson algebras. J. Algebra 313 (1), 100–124 (2007)
S. Cheng, V.G. Kac, A new N = 6 superconformal algebra. Commun. Math. Phys. 186 (1), 219–231 (1997)
S. Cheng, V.G. Kac, Conformal modules. Asian J. Math. 1, 181–193 (1997). Erratum: 2, 153–156 (1998)
P.M. Cohn, Universal Algebra, 2nd edn. (Reidel, Dordrecht, Holland, 1985)
A. D’Andrea, V.G. Kac, Structure theory of finite conformal algebras. Selecta Math. 4, 377–418 (1998)
D. Fattori, V.G. Kac, Classification of finite simple Lie conformal superalgebras. J. Algebra 258 (1), 23–59 (2002)
P. Grozman, D. Leites, I. Shchepochkina, Lie superalgebras of string theories. Acta Math. Vietnam 26 (1), 27–63 (2001)
N. Jacobson, Structure and Representation of Jordan Algebras (American Mathematical Society, Providence, RI, 1969)
V. Kac, Classification of infinite-dimensional simple linearly compact lie superalgebras. Adv. Math. 139, 1–55 (1998)
V.G. Kac, Vertex Algebras for Beginners. University Lecture Series, vol. 10, 2nd edn. American Mathematical Society, Providence, RI, 1998
V.G. Kac, J.W. van de Leur, On classification of superconformal algebras, in Strings, vol. 88 (World Scientific, Singapore, 1989), pp. 77–106
V.G. Kac, C. Martínez, E. Zelmanov, Graded simple Jordan Superalgebras of growth one. Mem. Am. Math. Soc. 150 (2001), X+140 pp.
I.L. Kantor, Some generalizations of Jordan algebras. Trudy Sem. Vektor. Tenzor. Anal. 16, 407–499 (1972)
I.L. Kantor, Connections between Poisson brackets and Jordan and Lie superalgebras, in Lie Theory, Differential Equations and Representation Theory (Univ. Montréal, Montréal, 1990), pp. 213–225
D. King, K. McCrimmon, The Kantor construction of Jordan superalgebras. Commun. Algebra 20 (1), 109–126 (1992)
M. Koecher, Imbeddings of Jordan algebras in Lie algebras. Am. J. Math. 89, 787–815 (1967)
A.I. Mal’cev, Algebraic Systems (Springer, New York, Heidelberg, 1973)
C. Martin, A. Piard, Classification of the indecomposable bounded modules over the Virasoro Lie algebra with weight spaces of dimension not exceeding two. Commun. Math. Phys. 150 (3), 465–493 (1992)
C. Martínez, E. Zelmanov, Simple finite-dimensional Jordan Superalgebras in prime characteristic. J. Algebra 236 (2), 575–629 (2001)
C. Martínez, E. Zelmanov, Representation theory of Jordan superalgebras I. Trans. Am. Math. Soc. 362 (2), 815–846 (2010)
C. Martínez, E. Zelmanov, Irreducible representations of the exceptional Cheng-Kac superalgebra. Trans. Am. Math. Soc. 366 (11), 5853–5876 (2014)
O. Mathieu, Classification of Harish-Chandra modules over the Virasoro algebra. Invent. Math. 107 (2), 225–234 (1992)
J. Tits, Une class d’algèbres de Lie en relation avec les algèbres de Jordan. Indag. Math. 24, 530–535 (1962)
E. Zelmanov, Lie algebras with finite gradation. Mat. Sb. 124 (3), 352–392 (1984)
E. Zelmanov, On the structure of conformal algebras. Contemp. Math. 264, 139–153 (2000)
Acknowledgements
Consuelo Martínez is partially supported by MTM 2013-45588-C3-1-P. Efim Zelmanov is partially supported by the National Science Foundation of the USA.
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Martı́nez, C., Zelmanov, E. (2016). Graded Modules over Superconformal Algebras. In: Gueye, C., Molina, M. (eds) Non-Associative and Non-Commutative Algebra and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 160. Springer, Cham. https://doi.org/10.1007/978-3-319-32902-4_3
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DOI: https://doi.org/10.1007/978-3-319-32902-4_3
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