On nn-translation algebras

Motivated by Iyama's higher representation theory, we introduce $n$-translation quivers and $n$-translation algebras. The classical $\mathbb Z Q$ construction of the translation quiver is generalized to construct an $(n+1)$-translation quiver from an $n$-translation quiver, using trivial extension and smash product. We prove that the quadratic dual of $n$-translation algebras have $(n-1)$-almost splitting sequences in the category of its projective modules. We also present a non-Koszul $1$-translation algebra whose trivial extension is $2$-translation algebra, thus also provides a class of examples of $(3,m-1)$-Koszul algebras (and also a class of $(m-1,3)$-Koszul algebras) for all $m \ge 2$.Comment: The paper is revised, according to the referees' suggestions and comments. The definitions of $n$-translation quiver, admissibility are rewritten, and the results related to these definition are revised. The results concerning $n$-almost split sequence is revised. The Section 7 is removed and Section 6 is split into 3 sections. The mistake and typos pointed out are correcte

Coverings and Truncations of Graded Selfinjective Algebras

Let $\Lambda$ be a graded self-injective algebra. We describe its smash product \Lambda# k\mathbb Z^* with the group $\mathbb Z$, its Beilinson algebra and their relationship. Starting with $\Lambda$, we construct algebras with finite global dimension, called $\tau$-slice algebras, we show that their trivial extensions are all isomorphic, and their repetitive algebras are the same \Lambda# k\mathbb Z^*. There exist $\tau$-mutations similar to the BGP reflections for the $\tau$-slice algebras. We also recover Iyama's absolute $n$-complete algebra as truncation of the Koszul dual of certain self-injective algebra.Comment: Manuscript revised, introduction and abstract rewritte

Monomial ideals under ideal operations

In this paper, we show for a monomial ideal $I$ of $K[x_1,x_2,\ldots,x_n]$ that the integral closure \ol{I} is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if $I$ has the same property. We also show that the $k^{th}$ symbolic power $I^{(k)}$ of $I$ preserves the properties of Borel type, Borel-fixed and strongly stable, and $I^{(k)}$ is lexsegment if $I$ is stably lexsegment. For a monomial ideal $I$ and a monomial prime ideal $P$, a new ideal $J(I, P)$ is studied, which also gives a clear description of the primary decomposition of $I^{(k)}$. Then a new simplicial complex $_J\bigtriangleup$ of a monomial ideal $J$ is defined, and it is shown that $I_{_J\bigtriangleup^{\vee}} = \sqrt{J}$. Finally, we show under an additional weak assumption that a monomial ideal is universal lexsegment if and only if its polarization is a squarefree strongly stable ideal.Comment: 18 page

Composition and growth effects of the current account: a synthesized portfolio view

This paper analyzes a useful accounting framework that breaks down the current account to two components: a composition effect and a growth effect. We show that past empirical evidence, which strongly supports the growth-eect as the main driver of current account dynamics, is mis- conceived. The remarkable empirical success of the growth eect is driven by the dominance of the cross-sectional variation, which, under conditions met by the data, is generated by an accounting approximation. In contrast to previous ndings that the portfolio share of net foreign assets to total assets is constant in a country, both our theoretical and empirical results support a highly persistent process or a unit root process, with some countries displaying a trend. Finally, we reestablish the composition effect as the quantitatively dominant driving force of current account dynamics in the past data