A型扩张仿射李代数的极大子代数

Maximal Subalgebras of Extended Affine Lie Algebra of Type A

设S是欧式空间R^n上的最小半格,由Jordan代数J(S)通过TKK构造可得到一个称之为TKK代数的李代数T(J(S)).进一步,可由TKK李代数T(J(S))得到一个A_1型、零度为v,且带有扩张仿射根系R(A_1,S)的扩张仿射李代数T.研究了扩张仿射李代数T的极大子代数,并得到了它的四类极大子代数.

Let T~ be the extended affine Lie algebra of type A1 and of nullity v with extended affine root system R（A1 ,S）,which is constructed from a TKK Lie algebra T（J（S））obtained from the Jordan algebra J （S）by the so-called Tits-Kantor-Koecher construction,where S is the 〞smallest〞 semilattice in Euclid-ean space Rn .In this paper,we study maximal subalgebras of extended affine Lie algebra T~ and obtain four kinds of maximal subalgebras.