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Let U(g) be the enveloping algebra of a finite dimensional reductive Lie algebra g over an algebraically closed field of prime characteristic. Let U?,P(s:) be the simply connected quantum enveloping algebra at the root of unity ? , of a complex semi-simple finite dimensional Lie algebra s:. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic. 相似文献
36.
Michael Eastwood Petr Somberg Vladimír Sou
ek 《Journal of Geometry and Physics》2007,57(12):2539-2546
Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case sl(2,C), there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter. 相似文献
37.
《Physics letters. A》2020,384(17):126349
We consider the quantization procedure and investigate the application of the quantizer–dequantizer method and star-product technique to construct associative products and the associative algebras formed by the quantizer–dequantizer operators and their symbols. The corresponding Lie algebras are also constructed. We study the case where the quantizer–dequantizer operators form a self-dual system and show that the structure constants of the Lie algebras satisfy some identity, in addition to the Jacobi identity. Using tomographic quantizer–dequantizer operators and their symbols, we construct the continuous associative algebra and the corresponding Lie algebra. 相似文献
38.
Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra. 相似文献
39.
A relation between quantum R-matrices and certain factorization problem in Hopf algebras is established. A definition of dressinf transformation in the quantum case is also given. 相似文献
40.
Rasoul Ahangari Maleki 《代数通讯》2017,45(2):514-520