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 s...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 ?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 ?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 ?2-graded automorphisms of the TKK algebra T(J(S)).展开更多
In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, condition...In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, conditions for these modules to be unitary are determined.展开更多
Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the ...Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.展开更多
基金the National Natural Science Foundation of China (Grant No.10671160)
文摘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 ?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 ?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 ?2-graded automorphisms of the TKK algebra T(J(S)).
基金supported by National Natural Science Foundation of China (Grant No.10931006)the PhD Programs Foundation of Ministry of Education of China (Grant No. 20100121110014)
文摘In this paper, we give explicit realizations for the irreducible integrable modules, which were clas- sified in Chang and Tan [Pacific J Math, 2011, 252: 293-312], of the extended baby TKK algebra. Moreover, conditions for these modules to be unitary are determined.
基金Supported by National Natural Science Foundation of China （Grant No. 10931006） and Foundation of Educational Department of Hubei Province in China （Grant No. B200529001） The author is grateful to the referee for some helpful suggestions.
文摘Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R（A1, S）, where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T（J（S）） which is obtained from the Jordan algebra ,：7（S） by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T（J（S））, where S is the ＂smallest＂ semilattice in Euclidean space Rn.
