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Let A n be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over A n . By further exploring the relationship between the Poincar′e series and the dimension and the multiplicity of M , we are able to prove that the tensor product of two finitely generated modules over A n has the multiplicity equal to the product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of A n . 相似文献
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Let H = uq(sl(2)) or u(sl(2)). By means of the standard basis of polynomial algebras, the Glebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of V(1)^n into the direct sum of simple modules is given in this paper. 相似文献
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有限维路代数的K_1群 总被引:1,自引:0,他引:1
本文通过计算有限维路代数k△的单位群和单位群的阿贝尔化,完全刻划了 任意域上有限维路代数的K1群. 相似文献
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设H是域k上的Hopf代数.本文首先讨论了量子Yang-BaxterH-余模与Yang-Baxter方程的解的关系;然后作为应用,给出了任意Hopf代数上Yang-Baxter方程的一个解. 相似文献
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设H是域k上的Hopf代数。本文首先讨论了量子Yang-Baxter H-余模与Yang-Baxter方程的解的关系;然后作为应用,给出了任意Hopf代数上Yang-Baxter方程的一个解。 相似文献
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1Intr0ducti0nThegreatattentiontotheQuantumYangBaxterEquation(QYBE)wasfirstlystimulatedbytheinversescatteringpr0blemmethodl5'6].Thenitturnedoutthatmanyofothermathe-maticalobjectsandphysicalm0delsareconnectedwiththeQYBE.Attemptstofindsoluti0nsoftheQYBEinasystematicwayhaveledtothetheoryofquantumgroups[61,andmanypapersaredev0tedtotheconstructionofthesolution,e.g.,8ee[7-10]-Inthispaper,wereviewananaloguetoquantumYang-Baxtermodule['1'1,thatis,quan-tumcomodule.wedevelopsolution8oftheQYBEaPp… 相似文献
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Verlinde模性范畴上的Casimir数及其应用 总被引:1,自引:0,他引:1
本文计算了秩为n+1的一类特殊的Verlinde模性范畴L的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr(L)_Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式E_(n+1)(X)在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickson多项式的有关因式分解定理,本文完全给出了Grothendieck代数Gr(L)_Z K的Jacobson根. 相似文献
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Let A n be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over A n . By further exploring the relationship between the Poincar′e series and the dimension and the multiplicity of M , we are able to prove that the tensor product of two finitely generated modules over A n has the multiplicity equal to the product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of A n . 相似文献