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
Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie ...Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.展开更多
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 determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor d...In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.展开更多
In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any charac...In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.展开更多
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.
基金Supported by National Natural Science Foundation of China (Grant No. 10671160)the Education Department of Fujian Province (Grant No. JBS07087)
文摘Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.
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)).
文摘In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrodinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig（a, b）.
基金This work was supported by the National Natural Science Foundation of China,Hundred Talents Program of Chinese Academy of Sciences and a Fund from National Education Ministry of China. Su Yucai was partially supported by Academy of Mathematics and Syst
文摘In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.
