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Let g be a finite dimensional complex simple classical Lie superalgebra and A be a commutative, associative algebra with unity over C. In this paper we define an integral form for the universal enveloping algebra of the map superalgebra g⊗A, and exhibit an explicit integral basis for this integral form. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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For a simple complex Lie algebra g we study the space of invariants A=(?g?⊗g?)g, which describes the isotypic component of type g in ?g?, as a module over the algebra of invariants (?g?)g. As main result we prove that A is a free module, of rank twice the rank of g, over the exterior algebra generated by all primitive invariants in (?g?)g, with the exception of the one of highest degree. 相似文献
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We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献
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Let F be either the real number field R or the complex number field C and RPn the real projective space of dimension n. Theorems A and C in Hemmi and Kobayashi (2008) [2] give necessary and sufficient conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m?n. In this paper, we simplify the theorems and apply them to the tangent bundle of RPn, its complexification, the normal bundle associated to an immersion of RPn in Rn+r(r>0), and its complexification. Our result for the normal bundle is a generalization of Theorem A in Kobayashi et al. (2000) [8] and that for its complexification is a generalization of Theorem 1 in Kobayashi and Yoshida (2003) [5]. 相似文献
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Nguyen Quang Dieu Pham Hien Bang Nguyen Xuan Hong 《Journal of Mathematical Analysis and Applications》2014
Let u,v be m-subharmonic functions defined on a domain Ω in Cn. We are interested in giving sufficient conditions on u,v such that u=v on the whole domain Ω. Some applications to weak convergence of sequence of m-subharmonic functions are also discussed. 相似文献
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The problems of computing single-valued, analytic branches of the logarithm and square root functions on a bounded, simply connected domain S are studied. If the boundary ∂S of S is a polynomial-time computable Jordan curve, the complexity of these problems can be characterized by counting classes #P, MP (or MidBitP ), and ⊕P: The logarithm problem is polynomial-time solvable if and only if FP=#P. For the square root problem, it has been shown to have the upper bound PMP and lower bound P⊕P. That is, if P=MP then the square root problem is polynomial-time solvable, and if P≠⊕P then the square root problem is not polynomial-time solvable. 相似文献
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