文献[1]从Euclid空间R^v(v≥1)的一个半格S出发,定义了一个Jordan代数J(S):然后通过Tits—Kantor-Koecher方法由J(S)构造出Lie代数G(J(S)).最后利用G(J(S))得到A1型扩张仿射Lie代数L(J(S)).本文给出v=2,S为格时。A1型扩张仿射Lie代数L(J(S))的Z^2一分次自同构群.
The authers of [1] define a unitary Jordan algebra J(S) from a semilattice S of Rv (v ≥ 1), and then construct Lie algebra G(J(S)) from the Jordan algebra J(S) by the so-called Tits- Kantor-Koecher construction, last obtain the extended affine Lie algebra of type -A1 (J(S)) from G(J(S)). in this paper we study the Z^2-graded automorphism group of L(J(S)) when v = 2, S is lattice.