19,377 research outputs found
Universal central extensions of twisted forms of split simple Lie algebras over rings
We give sufficient conditions for the descent construction to be the
universal central extension of a twisted form of a split simple Lie algebra
over a ring. In particular, the universal central extensions of twisted
multiloop Lie tori are obtained by the descent construction
Universal central extensions of over -graded algebras
We study central extensions of the Lie superalgebra , where
is a -graded superalgebra over a commutative ring . The Steinberg Lie
superalgebra plays a crucial role. We show that is
a central extension of for . We use a -graded
version of cyclic homology to show that the center of the extension is
isomorphic to as -modules. For , we prove that
is the universal central extension of . For
, we prove that and are both centrally
closed. The universal central extension of is constructed
explicitly.Comment: 18 pages; section 7 added; reference [KT] added; the authors thank
the referee for comments on the previous versio
Universal central extensions of direct limits of Lie superalgebras
We show that the universal central extension of a direct limit of perfect Lie
superalgebras L_i is (isomorphic to) the direct limit of the universal central
extensions of L_i. As an application we describe the universal central
extensions of some infinite rank Lie superalgebras
Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"
This special issue collects contributions from the participants of the
"Information in Dynamical Systems and Complex Systems" workshop, which cover a
wide range of important problems and new approaches that lie in the
intersection of information theory and dynamical systems. The contributions
include theoretical characterization and understanding of the different types
of information flow and causality in general stochastic processes, inference
and identification of coupling structure and parameters of system dynamics,
rigorous coarse-grain modeling of network dynamical systems, and exact
statistical testing of fundamental information-theoretic quantities such as the
mutual information. The collective efforts reported herein reflect a modern
perspective of the intimate connection between dynamical systems and
information flow, leading to the promise of better understanding and modeling
of natural complex systems and better/optimal design of engineering systems
- β¦