Automorphisms Of The Borel Subalgebras Of Chevalley Algebras Over Communicative Rings

Let R be a communicative ring with identity 1_r. Let B(R) be the Borel subal-gebra of the chevalley algebra of type L over R. And assume that 2 is a unit when L is B_n(n ≥ 3), D_n(n ≥ 4), E₆, E₇ or E₈; and 2,3 are units when L is B₂, C_n(n ≥ 3), F₄ or G₂. In this paper, we determine the automorphism group of B(R).If L is A_n(n ≥ 3), D_n(n ≥ 4) or E₆, any automorphism φ of B(R) can be expressed as φ = g · d_x · σ, where g, d_x and σ are graph, diagonal and inner automorphisms, respectively, of B(R).If L is B_n(n ≥ 2), C_n(n ≥ 3), E₇, E₈, F₄, or G₂, any automorphism φ of B(R) can be expressed as φ = d_x · σ.For the cases of A₁ and A₂, we also determine the automorphism group of B(R).