Derivations Of The Parabolic Ubalgebras Of The Lie Algebra Of Type B_n Over A Commutative Ring

Let n>1be a positive integer, R be an arbitrary commutative ring with identity, and2be invertible in R. Let so(N, R) where N=2n+1be the Lie algebra of type B_nover the ringR. In this paper, we first describe the parabolic subalgebras of so(N, R) by orthogonal flagsof ideals of R, and then prove that the derivations of the parabolic subalgebras of so(N, R)are all inner derivations.