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

Abstract

Let Cl+1(R) be the 2(l+1)×2(l+1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then tl+1CR = {m-1m-20-m-1T ∣ m̅1 is an l+1 upper triangular matrix, m̅2T=m̅2, over R} is the solvable subalgebra of Cl+1(R). In this paper, we give an explicit description of the automorphism group of tl+1(C)(R).