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Automorphisms of the standard Borel subalgebra of Lie algebra of \(C_m\) type over a commutative ring. (English) Zbl 1159.17002

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)].

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

Citations:

Zbl 1127.17011
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References:

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