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【期刊论文】SIMPLE LIE COLOR ALGEBRAS OF WEYL TYPE1
苏育才, Yucai Su* , Kaiming Zhao† and Linsheng Zhu‡
(appeared in Israel Journal of Mathematics, 137 (2003), 109-123),-0001,():
-1年11月30日
Abstract. For an (є; Ґ)-color-commutative associative algebra A with an identity element over a field F of characteristic not 2, and for a color-commutative color-derivation subalgebra D of A, denote by A[D] the associative subalgebra of End(A) generated by A (regarding as operators on A via multiplication) and D. It is proved that, as an associative algebra, A[D] is Ґ-graded simple if and only if A is Ґ-graded D-simple. Suppose A is Ґ-graded D-simple. Then, (a) A[D] is a free left A-module; (b) as a Lie color algebra, the subquotient [A[D];A[D]]=Z(A[D])\[A[D];A[D]] is simple (except one minor case), where Z(A[D]) is the color center of A[D]. The structure of this subquotient is explicitly described.
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【期刊论文】Generalized Virasoro and super-Virasoro algebras and modules of the intermediate series
苏育才, Yucai Su a and Kaiming Zhao b, *
Journal of Algebra 252(2002)1-19,-0001,():
-1年11月30日
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【期刊论文】Quasifinite representations of a family of Lie algebras of Block type ☆
苏育才, Yucai Su a a, b, *
Journal of Pure and Applied Algebra 192(2004)293-305,-0001,():
-1年11月30日
To any nonzero additive subgroup G of an algebraically closed %eld F of characteristic zero and s=0; 1, there corresponds a Lie algebra B(s;G) of Block type, with basis {xa; i|a ∈G, i ∈ Z+}, and relation [xa; i; xb; j]=s(b−a)xa+b; i+j +((a−1+s)j−(b−1+s)i)xa+b; i+j−1. In this paper, it is proved that B(s;G) has a nontrivial quasi%nite module if and only if s =1 and G is isomorphic to Z, and that a quasi%nite B(1; Z)-module is a highest or lowest weight module. Furthermore, the quasi%nite irreducible highest weight B(1; Z)-modules are classi%ed and the unitary ones are proved to be trivial.
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【期刊论文】Low dimensional cohomology of general conformal algebras gcN
苏育才, Yucai Su a)
J. Math. Phys., Vol. 45, No.1, January 2004,-0001,():
-1年11月30日
We compute the low dimensional cohomologies H q(gcN,C), Hq(gcN,C) of the infinite rank general Lie conformal algebras gcN with trivial coefficients for q<3, N51 or q<2, N>2. We also prove that the cohomology of gcN with coeffi-cients in its natural module is trivial, i.e., H*(gcN,C[э]N)=0, and thus partially solve an open problem of Bakalov-Kac-Voronov
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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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