Generalized Hopf-Ore extensions

We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore extension. We describe the generalized Hopf-Ore extensions of the enveloping algebras of Lie algebras. For some Lie algebras g, the generalized Hopf-Ore extensions of U(g) are classified.Comment: 21pages,Revised argument in section

Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\chi$ is a $k$-valued character for $G$ with $\chi(a)\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over $H'$ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over $H$ and $H'$, and classify them. Finally, when $\chi(a)$ is a primitive $n$-th root of unity for some $n>2$, we determine all finite dimensional indecomposable projective objects in the category of weight modules over $H'$.Comment: arXiv admin note: substantial text overlap with arXiv:1206.394

Trade and Workers: Evidence from the Philippines

We combine labor force survey data with trade and production data to examine the impact of trade on wages and employment in the Philippines' manufacturing section. Our main finding are as follows. First, in contrast to findings typically reported for Latin American countries, our data indicate that wage inequality in the Philippines' manufacturing sector has declined over the period in which trade liberalization has been undertaken. This is despite the fact that reductions in tariff rates were largest in less skill intensive manufacturing industries. There has also been an absence of any secular rise in returns to higher education. Second, tariff reductions have been associated with declines in industry wage premiums in capital-intensive industries. Moreover, these declines appear to have been largest for skilled workers. Finally, tariff reductions have had an insignificant effect on both employment as well as the average hours of work of full-time employees across industries. These findings are consistent with a scenario where workers in capital-intensive industries, especially the more skilled ones, earned rents prior to trade liberalization; liberalization may have worked to erode these.