Low dimensional cohomology of general conformal algebras gcNgc_N

We compute the low dimensional cohomologies $\tilde H^q(gc_N,C)$, H^q(gc_N,\C) of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\le3, N=1$ or $q\le2, N\ge2$. We also prove that the cohomology of $gc_N$ with coefficients in its natural module is trivial, i.e., H^*(gc_N,\C[\ptl]^N)=0; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\it Comm. Math. Phys.,} {\bf200} (1999), 561-598].Comment: 18 page

Classification of derivation-simple color algebras related to locally finite derivations

We classify the pairs $(A,D)$ consisting of an $(\epsilon,\Gamma)$-olor-commutative associative algebra $A$ with an identity element over an algebraically closed field $F$ of characteristic zero and a finite dimensional subspace $D$ of $(\epsilon,\Gamma)$-color-commutative locally finite color-derivations of $A$ such that $A$ is $\Gamma$-graded $D$-simple and the eigenspaces for elements of $D$ are $\Gamma$-graded. Such pairs are the important ingredients in constructing some simple Lie color algebras which are in general not finitely-graded. As some applications, using such pairs, we construct new explicit simple Lie color algebras of generalized Witt type, Weyl type.Comment: 15 page

Structure of Divergence-Free Lie Algebras

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with respect to the derivation subalgebra.Comment: 36 pages; Latex fil

Introduction

If Hong Kong were easy to simplify, this would have simplified things. Who is a ‘native’ resident? Or, to put the question another way, who is a ‘Hong Kong people’, a common second-language error here that raises interesting and rather profound questions when one unpacks the meaning underneath the Chinglish. Can people other than Cantonese-speaking Chinese fit the definition? Questions like these, as they have played out in the courts and the media, have led to shouting in the streets. And without the editors explicitly naming identity as a focus of this book (it is, after all, a fiction anthology, not a collection of essays in one of the social sciences), identity manifested as a theme in every story we accepted and quite a few that we did not