Conformal derivations of semidirect products of Lie conformal algebras and their conformal modules

Guo, Jiancang; Tan, Youjun

doi:10.1090/S0002-9939-2014-11880-6

Conformal derivations of semidirect products of Lie conformal algebras and their conformal modules
HTML articles powered by AMS MathViewer

by Jiancang Guo and Youjun Tan PDF

Proc. Amer. Math. Soc. 142 (2014), 1471-1483 Request permission

Abstract:

Conformal derivations from Lie conformal algebras to their conformal modules are used to describe conformal derivations of Lie conformal algebras of semidirect product type.

References

Bojko Bakalov, Alessandro D’Andrea, and Victor G. Kac, Theory of finite pseudoalgebras, Adv. Math. 162 (2001), no. 1, 1–140. MR 1849687, DOI 10.1006/aima.2001.1993
Bojko Bakalov, Victor G. Kac, and Alexander A. Voronov, Cohomology of conformal algebras, Comm. Math. Phys. 200 (1999), no. 3, 561–598. MR 1675121, DOI 10.1007/s002200050541
Shun-Jen Cheng and Victor G. Kac, Conformal modules, Asian J. Math. 1 (1997), no. 1, 181–193. MR 1480993, DOI 10.4310/AJM.1997.v1.n1.a6
Shun-Jen Cheng, Victor G. Kac, and Minoru Wakimoto, Extensions of conformal modules, Topological field theory, primitive forms and related topics (Kyoto, 1996) Progr. Math., vol. 160, Birkhäuser Boston, Boston, MA, 1998, pp. 79–129. MR 1653022
Alessandro D’Andrea and Victor G. Kac, Structure theory of finite conformal algebras, Selecta Math. (N.S.) 4 (1998), no. 3, 377–418. MR 1654574, DOI 10.1007/s000290050036
Alberto De Sole, Pedram Hekmati, and Victor G. Kac, Calculus structure on the Lie conformal algebra complex and the variational complex, J. Math. Phys. 52 (2011), no. 5, 053510, 35. MR 2839091, DOI 10.1063/1.3580676
Alberto De Sole and Victor G. Kac, Lie conformal algebra cohomology and the variational complex, Comm. Math. Phys. 292 (2009), no. 3, 667–719. MR 2551791, DOI 10.1007/s00220-009-0886-1
Davide Fattori, Victor G. Kac, and Alexander Retakh, Structure theory of finite Lie conformal superalgebras, Lie theory and its applications in physics V, World Sci. Publ., River Edge, NJ, 2004, pp. 27–63. MR 2172172, DOI 10.1142/9789812702562_{0}002
Victor Kac, Vertex algebras for beginners, 2nd ed., University Lecture Series, vol. 10, American Mathematical Society, Providence, RI, 1998. MR 1651389, DOI 10.1090/ulect/010
Pavel Kolesnikov, On finite representations of conformal algebras, J. Algebra 331 (2011), 169–193. MR 2774653, DOI 10.1016/j.jalgebra.2010.12.014
P. S. Kolesnikov, Simple associative conformal algebras of linear growth, J. Algebra 295 (2006), no. 1, 247–268. MR 2188860, DOI 10.1016/j.jalgebra.2005.08.004
P. S. Kolesnikov, Associative conformal algebras with finite faithful representation, Adv. Math. 202 (2006), no. 2, 602–637. MR 2222361, DOI 10.1016/j.aim.2005.04.001
Alexander Retakh, Structure and representations of conformal algebras, Algebras, rings and their representations, World Sci. Publ., Hackensack, NJ, 2006, pp. 289–311. MR 2234312, DOI 10.1142/9789812774552_{0}018
Alexander Retakh, Associative conformal algebras of linear growth, J. Algebra 237 (2001), no. 2, 769–788. MR 1816715, DOI 10.1006/jabr.2000.8616
Michael Roitman, Universal enveloping conformal algebras, Selecta Math. (N.S.) 6 (2000), no. 3, 319–345. MR 1817616, DOI 10.1007/PL00001391
Yucai Su and Xiaoqing Yue, Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $\textrm {gc}_1$, J. Algebra 340 (2011), 182–198. MR 2813568, DOI 10.1016/j.jalgebra.2011.06.001