2,048 research outputs found

    Abelian and non-abelian second cohomologies of quantized enveloping algebras

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    For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology that derives information from the non-abelian second cohomology classifying cleft extensions. As a sample computation, a quantum analogue of Whitehead's second lemma for Lie-algebra cohomology is proved.Comment: 40 Pages, the final version to appear in J. Algebra; mainly, typos correcte

    Interfaces between statistical analysis packages and the ESRI geographic information system

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    Interfaces between ESRI's geographic information system (GIS) data files and real valued data files written to facilitate statistical analysis and display of spatially referenced multivariable data are described. An example of data analysis which utilized the GIS and the statistical analysis system is presented to illustrate the utility of combining the analytic capability of a statistical package with the data management and display features of the GIS

    The Noether problem for Hopf algebras

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    In previous work, Eli Aljadeff and the first-named author attached an algebra B_H of rational fractions to each Hopf algebra H. The generalized Noether problem is the following: for which finite-dimensional Hopf algebra H is B_H the localization of a polynomial algebra? A positive answer to this question when H is the algebra of functions on a finite group implies a positive answer for the classical Noether problem for the group. We show that the generalized Noether problem has a positive answer for all pointed finite-dimensional Hopf algebras over a field of characteristic zero. We actually give a precise description of B_H for such a Hopf algebra, including a bound on the degrees of the generators. A theory of polynomial identities for comodule algebras over a Hopf algebra H gives rise to a universal comodule algebra whose subalgebra of coinvariants V_H maps injectively into B_H. In the second half of this paper, we show that B_H is a localization of V_H when again H is a pointed finite-dimensional Hopf algebra in characteristic zero. We also report on a result by Uma Iyer showing that the same localization result holds when H is the algebra of functions on a finite group.Comment: 19 pages. Section 4.3 and three references have been added to Version
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