48,867 research outputs found
Contractions, Hopf algebra extensions and cov. differential calculus
We re-examine all the contractions related with the
deformed algebra and study the consequences that the contraction process has
for their structure. We also show using
as an example that, as in the undeformed case, the contraction may generate
Hopf algebra cohomology. We shall show that most of the different Hopf algebra
deformations obtained have a bicrossproduct or a cocycle bicrossproduct
structure, for which we shall also give their dual `group' versions. The
bicovariant differential calculi on the deformed spaces associated with the
contracted algebras and the requirements for their existence are examined as
well.Comment: TeX file, 25 pages. Macros are include
Effective actions, relative cohomology and Chern Simons forms
The explicit expression of all the WZW effective actions for a simple group G
broken down to a subgroup H is established in a simple and direct way, and the
formal similarity of these actions to the Chern-Simons forms is explained.
Applications are also discussed.Comment: 11 pages. Latex2e file. Published versio
Self-organized evolution in socio-economic environments
We propose a general scenario to analyze social and economic changes in
modern environments. We illustrate the ideas with a model that incorporating
the main trends is simple enough to extract analytical results and, at the same
time, sufficiently complex to display a rich dynamic behavior. Our study shows
that there exists a macroscopic observable that is maximized in a regime where
the system is critical, in the sense that the distribution of events follow
power-laws. Computer simulations show that, in addition, the system always
self-organizes to achieve the optimal performance in the stationary state.Comment: 4 pages RevTeX; needs epsf.sty and rotate.sty; submitted to Phys Rev
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