13,725 research outputs found
Vitality and Modernity: Defining the “Folk” in Early Twentieth Century China
As usual, the 2005 Chinese Rooster New Year celebrations in Beijing highlighted the annual Earth Temple Fair (Ditan Miaohui) as an indispensable attraction. In recent years, this entertaining space featuring red lanterns, lion dances, and revived folk performances has been widely and officially advocated as an occasion and place to appreciate “national culture (minzu wenhua)” and to experience “folk culture (minsu wenhua).” In the commodified and globalized metropolitan capital of the nation, the Fair forms a symbolic space where traditionality is celebrated to label national identity. [excerpt
Redefining Sovereignty in International Economic Law (Book Review)
Book review of Wenhua Shan, Penelope Simons and Dalvinder Singh (Eds.) Redefining Sovereignty in International Economic Law. Oxford and Portland, Oregon: Hart Publishing, 2008published_or_final_versio
A Generalization of Mathieu Subspaces to Modules of Associative Algebras
We first propose a generalization of the notion of Mathieu subspaces of
associative algebras , which was introduced recently in [Z4] and
[Z6], to -modules . The newly introduced notion in a
certain sense also generalizes the notion of submodules. Related with this new
notion, we also introduce the sets and of stable elements
and quasi-stable elements, respectively, for all -subspaces of -modules , where is the base ring of . We then
prove some general properties of the sets and .
Furthermore, examples from certain modules of the quasi-stable algebras [Z6],
matrix algebras over fields and polynomial algebras are also studied.Comment: A new case has been added; some mistakes and misprints have been
corrected. Latex, 31 page
Noncommutative Symmetric Systems over Associative Algebras
This paper is the first of a sequence papers ([Z4]--[Z7]) on the {\it
CS systems} over differential
operator algebras in commutative or noncommutative variables ([Z4]); the
CS systems over the Grossman-Larson Hopf algebras ([GL],[F]) of
labeled rooted trees ([Z6]); as well as their connections and applications to
the inversion problem ([BCW],[E4]) and specializations of NCSFs ([Z5],[Z7]). In
this paper, inspired by the seminal work [GKLLRT] on NCSFs (noncommutative
symmetric functions), we first formulate the notion {\it CS
systems} over associative -algebras. We then prove some results for
CS systems in general; the CS systems over
bialgebras or Hopf algebras; and the universal CS system formed
by the generating functions of certain NCSFs in [GKLLRT]. Finally, we review
some of the main results that will be proved in the followed papers [Z4], [Z6]
and [Z7] as some supporting examples for the general discussions given in this
paper.Comment: A connection of NCS systems with combinatorial Hopf algebras of M.
Aguiar, N. Bergeron and F. Sottile has been added in Remark 2.17. Latex, 32
page
Differential Operator Specializations of Noncommutative Symmetric Functions
Let be any unital commutative -algebra and
commutative or noncommutative free variables. Let be a formal parameter
which commutes with and elements of . We denote uniformly by \kzz and
\kttzz the formal power series algebras of over and ,
respectively. For any , let \cDazz be the unital algebra
generated by the differential operators of \kzz which increase the degree in
by at least and \ataz the group of automorphisms
of \kttzz with and .
First, for any fixed and F_t\in \ataz, we introduce five
sequences of differential operators of \kzz and show that their generating
functions form a CS (noncommutative symmetric) system [Z4] over the
differential algebra \cDazz. Consequently, by the universal property of the
CS system formed by the generating functions of certain NCSFs
(noncommutative symmetric functions) first introduced in [GKLLRT], we obtain a
family of Hopf algebra homomorphisms \cS_{F_t}: {\mathcal N}Sym \to \cDazz
(F_t\in \ataz), which are also grading-preserving when satisfies
certain conditions. Note that, the homomorphisms \cS_{F_t} above can also be
viewed as specializations of NCSFs by the differential operators of \kzz.
Secondly, we show that, in both commutative and noncommutative cases, this
family \cS_{F_t} (with all and F_t\in \ataz) of differential
operator specializations can distinguish any two different NCSFs. Some
connections of the results above with the quasi-symmetric functions ([Ge],
[MR], [S]) are also discussed.Comment: Latex, 33 pages. Some mistakes and misprints have been correcte
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