2,048 research outputs found

### Abelian and non-abelian second cohomologies of quantized enveloping algebras

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

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

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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