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【期刊论文】Structure of Divergence-Free Lie Algebras
苏育才, Yucai Su Xiaoping Xu
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-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】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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苏育才, Yucai Su
Canad. J. Math. Vol. 55 (4), 2003 pp. 856-896,-0001,():
-1年11月30日
Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a "sandwich" method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson algebras are isomorphic. Furthermore, the derivation algebras and the second cohomology groups are determined.
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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】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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