Tang, Xiaomin; Xu, Jinli The derivation Lie algebra of the higher rank Virasoro-like algebra and its automorphism groups. (English) Zbl 1211.17019 Linear Algebra Appl. 430, No. 8-9, 2170-2181 (2009). 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 K. Zhao and D. Ž. Đoković [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)]. Reviewer: Olaf Ninnemann (Berlin) Cited in 2 Documents MSC: 17B65 Infinite-dimensional Lie (super)algebras 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras Keywords:higher-rank Virasoro-like algebra; derivation Lie algebra; skew derivation Lie algebra; automorphism group Citations:Zbl 0978.17015; Zbl 0929.17025 PDFBibTeX XMLCite \textit{X. Tang} and \textit{J. Xu}, Linear Algebra Appl. 430, No. 8--9, 2170--2181 (2009; Zbl 1211.17019) Full Text: DOI References: [1] Cao, Y.; Tan, Z., Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring, Linear Algebra Appl., 360, 1, 105-122 (2003) · Zbl 1015.17017 [2] Eick, B., Computing the automorphism group of a solvable Lie algebra, Linear Algebra Appl., 382, 1, 195-209 (2004) · Zbl 1045.17001 [3] Farnsteiner, R., Derivations and central extensions of finitely generated graded Lie algebras, J. Algebra, 118, 33-45 (1988) · Zbl 0658.17013 [4] Jiang, C.; Meng, D., The Automorphism Group of the Derivation Algebra of the Virasoro-like Algebra, Adv. Math. (China), 27, 2, 175-183 (1998) · Zbl 1054.17505 [5] Kirkman, E.; Procesi, C.; Small, L., A \(q\)-analog for the Virasoro algebra, Comm. Algebra, 22, 3755-3774 (1994) · Zbl 0813.17009 [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 [7] Mathieu, O., Classification of Harish-Chandra modules over the Virasoro algebra, Invent. Math., 107, 225-234 (1992) · Zbl 0779.17025 [8] Su, Y.; Zhu, L., Derivation algebras of centerless perfect Lie algebras are complete, J. Algebra, 285, 508-515 (2005) · Zbl 1154.17303 [9] Wang, X.; Zhao, K., Verma modules over the Virasoro-like algebra, J. Austral. Math., 80, 179-191 (2006) · Zbl 1109.17013 [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, 1, 139-153 (2006) · Zbl 1105.17006 [11] Ye, C.; Tan, S., Graded automorphism group of TKK algebra, Sci. China Ser. A, 51, 2, 161-168 (2008) · Zbl 1192.17014 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.