Yu, Qiu; Wang, Dengyin; Ou, Shikun Automorphisms of the standard Borel subalgebra of Lie algebra of \(C_m\) type over a commutative ring. (English) Zbl 1159.17002 Linear Multilinear Algebra 55, No. 6, 545-550 (2007). The authors describe all automorphisms of the standard Borel subalgebra of the symplectic algebra \(\text{sp}(2m,R)\), over a commutative ring \(R\) where \(2\) is invertible. Every automorphism is the product of an inner automorphism and what here and in related papers has been called an extremal automorphism. Analogous results for a Borel subalgebra, or related subalgebras such as the one generated by all positive root spaces, of Chevalley algebras of other types, have been obtained by various authors, see e.g. [Y. Cao, D. Jiang and J. Wang, Int. J. Algebra Comput. 17, No. 3, 527–555 (2007; Zbl 1127.17011)]. Reviewer: Sandro Mattarei (Povo) Cited in 1 Document MSC: 17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras 17B45 Lie algebras of linear algebraic groups 13C10 Projective and free modules and ideals in commutative rings Keywords:Lie algebra; automorphism; commutative ring Citations:Zbl 1127.17011 PDFBibTeX XMLCite \textit{Q. Yu} et al., Linear Multilinear Algebra 55, No. 6, 545--550 (2007; Zbl 1159.17002) Full Text: DOI References: [1] DOI: 10.1006/jabr.1994.1329 · Zbl 0822.17017 · doi:10.1006/jabr.1994.1329 [2] DOI: 10.1006/jabr.1996.6866 · Zbl 0878.17016 · doi:10.1006/jabr.1996.6866 [3] DOI: 10.1016/S0024-3795(02)00446-9 · Zbl 1015.17017 · doi:10.1016/S0024-3795(02)00446-9 [4] DOI: 10.1016/0024-3795(93)00255-X · Zbl 0826.16034 · doi:10.1016/0024-3795(93)00255-X [5] DOI: 10.1016/0021-8693(91)90206-N · Zbl 0729.16024 · doi:10.1016/0021-8693(91)90206-N [6] DOI: 10.1007/BF01194296 · Zbl 0601.16028 · doi:10.1007/BF01194296 [7] DOI: 10.1090/S0002-9947-1981-0594417-5 · doi:10.1090/S0002-9947-1981-0594417-5 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.