Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings

Abstract

LetCl+1(R)be the2(l+1)×2(l+1)matrix symplectic Lie algebra over a commutative ringRwith 2 invertible. Thentl+1CR  =  {m-1m-20-m-1T ∣ m̅1is anl+1upper triangular matrix,m̅2T=m̅2,  over  R}is the solvable subalgebra ofCl+1(R). In this paper, we give an explicit description of the automorphism group oftl+1(C)(R).