Abstract The generalized Broer-Kaup-Kupershmidt (generalized BKK) isospectral problem, including the x-derivative of potential, is considered based on Lie algebra A1. The variational trace identity is extended to construct Hamiltonian structure of generalized BKK system. The Lie algebra A1 is extended to the non-semi-simple Lie algebra of 4 × 4 matrix form, from which a hierarchy of soliton equ...

We construct the entire generalized Kac-Moody Lie algebra as a quotient of the positive part of another generalized Kac-Moody Lie algebra. The positive part of a generalized Kac-Moody Lie algebra can be constructed from representations of quivers using Ringel's Hall algebra construction. Thus we give a direct realization of the entire generalized Kac-Moody Lie algebra. This idea arises from the...

Suppose that G is a connected compact Lie group. We show that simple numerical information about the Weyl group of G can be used to obtain bounds, often sharp, on the size of the center of G. These bounds are obtained with the help of certain Coxeter elements in the Weyl group. Variants of the method use generalized Coxeter elements and apply to p-compact groups; in this case a splitting theore...

We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie...

ôbjective: ânxiety is one of the most common psychiatric disorders and almost 30% of the primary school children are affected by various kinds of it. group play therapy has been reported to be a useful component of treatment of generalized ânxiety disorder (gâd). the goal of this research was to determine the efficacy of this treatment in children with gâd. methods: ïn this quasi-experimental s...

In this work we introduce a concept of expansiveness for actions connected Lie groups. We study some its properties and investigate implications expansiveness. the centralizer expansive CW-expansiveness pseudo-group actions. As an application, prove positiveness geometric entropy foliations group

Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra sl(n, C) is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-gro...