Varieties of Superalgebras of Polynomial Growth

2010 Mathematics Subject Classification: 16R10, 16W55, 16P90.Let V^gr be a variety of associative superalgebras over a field F of characteristic zero. It is well-known that V gr can have polynomial or exponential growth. Here we present some classification results on varieties of polynomial growth. In particular we classify the varieties of at most linear growth and all subvarieties of the varieties of almost polynomial growth.∗ The author was partially supported by MIUR of Italy

Characterizing varieties of colength 644

Let A be an associative algebra over a field F of characteristic zero, and let n(A), n=1,2,, be the sequence of cocharacters of A. For every n1, let ln(A) denote the nth colength of A, counting the number of Sn-irreducibles appearing in n(A). In this article, we classify the algebras A such that the sequence of colengths ln(A), n=1,2,, is bounded by four. Moreover we construct a finite number of algebras A1,, Ad, such that ln(A)4 if and only if A1,, Ad var(A)

Essays in development economics and entrepreneurship

This dissertation consists of three chapters that study issues in Development Economics and Entrepreneurship. The first two chapters study the long-term consequences of civil conflict in developing countries using data from Rwanda; the third chapter examines determinants of science and non-science entrepreneurship for immigrants and natives in the United States. Chapter 1 investigates the impact of the 1994 Rwandan genocide on the probability that women become victims of intimate partner violence using detailed data on conflict intensity combined with a household survey collected after the genocide. Genocide intensity in the area of residence is associated with a higher probability of becoming victim of domestic violence for women who married after the genocide, but not for women who married before. Using census data collected before and after the conflict, I show that changes in local marriage market conditions likely caused by the genocide were a significant factor that contributed to increase domestic violence and reduce decision-making power for women who married after the genocide. Chapter 2 analyzes the long-term effect of the Rwandan genocide on education. Previous work showed that the genocide significantly decreased schooling for children who were in early childhood or in school during the genocide. I follow these children over time using recent data and I find that they eventually catch up to their peers. I also study the effect of the genocide on schooling for children born after the genocide. I observe a large, negative effect on educational achievement for children who are born up to five years after the end of the conflict. I explore potential mechanisms for this finding and I show that changes in marriage market conditions did not contribute to decrease educational attainment for children born after the genocide. In chapter 3, I use data from a large survey of scientists and highly educated individuals to show that conditional on standard factors, immigrants are significantly more likely to become entrepreneurs even after controlling for their relative position on the ability spectrum (measured by wage residuals). I find significant differences in the role of ability in science and non-science entrepreneurship for all individuals

Codimensions of algebras with additional structures

Let A be an associative algebra endowed with an automorphism or an antiautomorphism phi of order <= 2. One associates to A, in a natural way, a numerical sequence c(n)(phi)(A), n = 1, 2, ... , called the sequence of phi-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A. In [13] it was proved that such a sequence is eventually nondecreasing in case phi is an antiautomorphism. Here we prove that it still holds in case phi is an automorphism and present some recent results about the asymptotics of c(n)(phi)(A)

www.hicn.org Civil Conflict, Sex Ratio and Intimate Partner Violence in Rwanda 1

Abstract: This paper examines the long-term impact of civil conflict on intimate partner violence and women’s decision-making power using post-genocide data from Rwanda. Household survey data collected 11 years after the genocide indicate that women who became married after the genocide experienced significantly increased intimate partner violence and decreased decision-making power relative to women who became married before. The effect was greater for women in localities with high genocide intensity. I find that variation in the marriage market sex ratio across localities and over time explains part of the effect of the genocide on intimate partner violence. 1 I am grateful to Daniele Paserman, Claudia Olivetti and Dilip Mookherjee for support and guidance throughout thi