45,515 research outputs found
Coverings and Truncations of Graded Selfinjective Algebras
Let be a graded self-injective algebra. We describe its smash
product \Lambda# k\mathbb Z^* with the group , its Beilinson
algebra and their relationship. Starting with , we construct algebras
with finite global dimension, called -slice algebras, we show that their
trivial extensions are all isomorphic, and their repetitive algebras are the
same \Lambda# k\mathbb Z^*. There exist -mutations similar to the BGP
reflections for the -slice algebras. We also recover Iyama's absolute
-complete algebra as truncation of the Koszul dual of certain self-injective
algebra.Comment: Manuscript revised, introduction and abstract rewritte
On -translation algebras
Motivated by Iyama's higher representation theory, we introduce
-translation quivers and -translation algebras. The classical construction of the translation quiver is generalized to construct an
-translation quiver from an -translation quiver, using trivial
extension and smash product. We prove that the quadratic dual of
-translation algebras have -almost splitting sequences in the
category of its projective modules. We also present a non-Koszul
-translation algebra whose trivial extension is -translation algebra,
thus also provides a class of examples of -Koszul algebras (and also a
class of -Koszul algebras) for all .Comment: The paper is revised, according to the referees' suggestions and
comments. The definitions of -translation quiver, admissibility are
rewritten, and the results related to these definition are revised. The
results concerning -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
Monomial ideals under ideal operations
In this paper, we show for a monomial ideal of
that the integral closure \ol{I} is a monomial ideal of Borel type
(Borel-fixed, strongly stable, lexsegment, or universal lexsegment
respectively), if has the same property. We also show that the
symbolic power of preserves the properties of Borel type,
Borel-fixed and strongly stable, and is lexsegment if is stably
lexsegment. For a monomial ideal and a monomial prime ideal , a new
ideal is studied, which also gives a clear description of the primary
decomposition of . Then a new simplicial complex of
a monomial ideal is defined, and it is shown that
. 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
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