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The derivation Lie algebra of the higher rank Virasoro-like algebra and its automorphism groups. (English) Zbl 1211.17019
Authors’ summary: “We study the derivation Lie algebra of the higher rank Virasoro-like algebra. We prove that it is isomorphic to the skew derivation Lie algebra. We also characterize the automorphism groups of the higher rank Virasoro-like algebra and the skew derivation Lie algebra. This generalizes the result of some related references.” The main results are, however, special cases resp. easy consequences of two papers of {\it K. Zhao} and {\it D. Ž. \Dj oković} [J. Algebra 193, No. 1, 144--179 (1997; Zbl 0978.17015) and J. Pure Appl. Algebra 127, No. 2, 153--165 (1998; Zbl 0929.17025)].
17B65Infinite-dimensional Lie (super)algebras
17B40Automorphisms, derivations and other operators on Lie algebras
Full Text: DOI
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[6] Lin, W.; Tan, S.: Nonzero level harish -- chandra modules over the Virasoro-like algebra, J. pure appl. Algebra 204, 90-105 (2006) · Zbl 1105.17014 · doi:10.1016/j.jpaa.2005.03.002
[7] Mathieu, O.: Classification of harish -- chandra modules over the Virasoro algebra, Invent. math. 107, 225-234 (1992) · Zbl 0779.17025 · doi:10.1007/BF01231888
[8] Su, Y.; Zhu, L.: Derivation algebras of centerless perfect Lie algebras are complete, J. algebra 285, 508-515 (2005) · Zbl 1154.17303 · doi:10.1016/j.jalgebra.2004.09.033
[9] Wang, X.; Zhao, K.: Verma modules over the Virasoro-like algebra, J. austral. Math. 80, 179-191 (2006) · Zbl 1109.17013 · doi:10.1017/S1446788700013069
[10] Xue, M.; Lin, W.; Tan, S.; Extension, Central: Derivations and automorphism group for Lie algebras arising from the 2-dimensional torus, J. Lie theory 16, No. 1, 139-153 (2006) · Zbl 1105.17006 · http://www.heldermann.de/JLT/JLT16/JLT161/jlt16012.htm
[11] Ye, C.; Tan, S.: Graded automorphism group of TKK algebra, Sci. China ser. A 51, No. 2, 161-168 (2008) · Zbl 1192.17014 · doi:10.1007/s11425-007-0199-9