Graded automorphism group of TKK algebra

The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)).

Graded automorphism group of TKK algebra

The classification of extended affine Lie algebras of type A ₁ depends on the Tits-Kantor-Koecher (TKK) algebras constructed from semilattices of Euclidean spaces. One can define a unitary Jordan algebra J(S) from a semilattice S of ℝ^v (v ≥ 1), and then construct an extended affine Lie algebra of type A ₁ from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction. In ℝ² there are only two non-similar semilattices S and S’, where S is a lattice and S’ is a non-lattice semilattice. In this paper we study the ℤ²-graded automorphisms of the TKK algebra T(J(S)). This work was supported by the National Natural Science Foundation of China (Grant No. 10671160)