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【期刊论文】Derivations and structure of the Lie algebras of Xu type
苏育才, Yucai Su
manuscripta math. 105, 483-500 (2001),-0001,():
-1年11月30日
We determine the derivation algebras and the isomorphism classes of a family of the simple Lie algebras introduced recently by Xu [manuscripta math. 100, 489-518 (1999)]. The structure space of these algebras is given explicitly.
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【期刊论文】Structure of Divergence-Free Lie Algebras
苏育才, Yucai Su Xiaoping Xu
,-0001,():
-1年11月30日
One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally finite derivation subalgebra such that the commutative associative algebra is derivation-simple with respect to the derivation subalgebra.
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【期刊论文】Quasifinite representations of a Lie algebra of Block type
苏育才, Yucai Su
Journal of Algebra 276(2004)117-128,-0001,():
-1年11月30日
Let B be the Lie algebra of Block type over C with basis {Lα,i, C | α, i ∈ Z, i−1} and relations [Lα,i,Lβ,j] = ((i +1)β −(j +1)α)Lα+β,i+j +αδα+β,0δi+j,−2C, [C,Lα,i] = 0. In this paper, it is proved that a quasifinite irreducible B-module is a highest or lowest weight module. Furthermore, the quasifinite irreducible highest weight modules are classified and the unitary ones are proved to be trivial.
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【期刊论文】Classification of derivation-simple color algebras related to locally finite derivations
苏育才, Yucai Su Kaiming Zhao Linsheng Zhu
J. Math. Phys., Vol. 45, No.1, January 2004,-0001,():
-1年11月30日
We classify the pairs (A,D) consisting of an (e,ſ)-color-commutative associative algebra A with an identity element over an algebraically closed field F of characteristic zero and a finite dimensional subspace D of (e,ſ)-color-commutative locally finite color-derivations of A such that A is G-graded D-simple and the eigenspaces for elements of D are G-graded. Such pairs are the important ingredients in constructing some simple Lie color algebras which are in general not finitely-graded. As some applications, using such pairs, we construct new explicit simple Lie color algebras of generalized Witt type, Weyl type.
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【期刊论文】Simple Modules over the Higher-Rank Super-Virasoro Algebras
苏育才, YUCAI SU★
Letters in Mathematical Physics 53: 263-272, 2000.,-0001,():
-1年11月30日
It is proved that uniformly bounded simple modules over higher-rank super-Virasoro algebras are modules of the intermediate series, and that simple modules with finite dimensional weight spaces are either modules ofthe intermediate series or generalized highest weightmodules
higher-rank super-Virasoro algebra,, uniformly bounded module,, module of the intermediate series,, generalized highest weight module.,
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