Abstract
The loop-Witt algebra is the Lie algebra of the tensor product of the Witt algebra and the Laurent polynomial algebra. In this paper we study the universal central extension, derivations and automorphism group for the loop-Witt algebra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kac, V., Raina, A.: Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras, World Scientific, 1987
Mathieu, O.: Classification of Harish-Chandra modules over the Virasoro Lie algebra. Invent. Math., 107(1), 225–234 (1992)
Guo, X., Lu, R., Zhao, K.: Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra. Forum Math., 23(5), 1029–1052 (2011)
Billig, Y., Molev, A., Zhang, R.: Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus. Adv. Math., 218(6), 1972–2004 (2008)
Tang, X.: Subalgebras of the Lie algebra for the derivations on torus and their representations. Algebra Colloq., in press
Gao, S., Jiang, C., Pei, Y.: Derivations, central extensions and automorphisms of a Lie algebra. Acta Mathematica Sinica, Chinese Series, 52(2), 281–288 (2009)
Gao, Y.: Representations of extended affine Lie algebras coordinatized by certain quantum tori. Compos. Math., 123(1), 1–25 (2000)
Gao, Y., Shang, S.: Universal coverings of Steinberg Lie algebras of small characteristic. J. Algebra, 311(1), 216–230 (2007)
Lau, M.: Bosonic and fermionic representations of Lie algebra central extensions. Adv. Math., 194(2), 225–245 (2005)
Li, J., Su, Y., Zhu, L.: 2-Cocycles of original deformative Schrödinger-Virasoro algebras. Sci. China Ser. A, 51(11), 1989–1999 (2008)
Liu, D., Hu, N.: Universal central extensions of the matrix Leibniz superalgebras \(\mathfrak{s}\mathfrak{l}(\mathfrak{m},\mathfrak{n},\mathfrak{A})\). Comm. Algebra, 35(6), 1814–1823 (2007)
Lin, W., Tan, S.: Central extensions and derivations of the Lie algebras of skew derivations for the quantum torus. Comm. Algebra, 33(11), 3919–3938 (2005)
Tan, S., Zhang, X.: Automorphisms and Verma modules for generalized Schrödinger-Virasoro algebras. J. Algebra, 322(4), 1379–1394 (2009)
Xu, X.: Representations of centrally-extended Lie algebras over differential operators and vertex algebras. J. Pure Appl. Algebra, 212(6), 1253–1309 (2008)
Zeng, B.: The derivations and central extensions of a class of Lie algebras over quantum torus. Acta Mathematica Sinica, Chinese Series, 52(2), 163–170 (2009)
Chen, C., Lian, H., Tan, S.: Automorphism group and representation of a twisted multi-loop algebra. Acta Mathematica Sinica, English Series, 26(1), 143–154 (2010)
Humphreys, J.: Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972
Garland, H.: The arithmetic theory of loop groups. Publications Mathématiques de l’IH ÉS, 52(1), 5–136 (1980)
Weibel, C.: An Introduction to Homological Algebra, Cambridge Univ. Press, Cambridge, 1995
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported in part by National Natural Science Foundation of China (Grant No. 11171294), Natural Science Foundation of Heilongjiang Province of China (Grant No. A201013), Science Fundation for Distinguished Young Scholars of Heilongjiang Province of China (Grant No. JC201004), Postdoctoral Scientific Research Foundation of Heilongjiang Province (Grant No. LBH-Q08026) and the fund of Heilongjiang Education Committee (Grant No. 11541268)
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Tang, X.M., Zhang, Z. The structures for the loop-Witt algebra. Acta. Math. Sin.-English Ser. 28, 2329–2344 (2012). https://doi.org/10.1007/s10114-012-0161-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-012-0161-9