9,770 research outputs found
Automorphic Lie algebras with dihedral symmetry
No full textThe concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl2(C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits
Invariants of automorphic lie algebras
No full textAutomorphic Lie Algebras arise in the context of reduction groups introduced in the late 1970s [35] in the field of integrable systems. They are subalgebras of Lie algebras over a ring of rational functions, denied by invariance under the action of a finite group, the reduction group. Since their introduction in 2005 [29, 31], mathematicians aimed to classify Automorphic Lie Algebras. Past work shows remarkable uniformity between the Lie algebras associated to different reduction groups. That is, many Automorphic Lie Algebras with nonisomorphic reduction groups are isomorphic [4, 30]. In this thesis we set out to find the origin of these observations by searching for properties that are independent of the reduction group, called invariants of Automorphic Lie Algebras.
The uniformity of Automorphic Lie Algebras with nonisomorphic reduction groups starts at the Riemann sphere containing the spectral parameter, restricting the finite groups to the polyhedral groups. Through the use of classical invariant theory and the properties of this class of groups it is shown that Automorphic Lie Algebras are freely generated modules over the polynomial ring in one variable. Moreover, the number of generators equals the dimension of the base Lie algebra, yielding an invariant. This allows the definition of the determinant of invariant vectors which will turn out to be another invariant. A surprisingly simple formula is given expressing this determinant as a monomial in ground forms.
All invariants are used to set up a structure theory for Automorphic Lie Algebras. This naturally leads to a cohomology theory for root systems. A first exploration of this structure theory narrows down the search for Automorphic Lie Algebras signicantly. Various particular cases are fully determined by their invariants, including most of the previously studied Automorphic Lie Algebras, thereby providing an explanation for their uniformity.In addition, the structure theory advances the classification project. For example, it clarifies the effect of a change in pole orbit resulting in various new Cartan-Weyl normal form generators for Automorphic Lie Algebras. From a more general perspective, the success of the structure theory and root system cohomology in absence of a field promises interesting theoretical developments for Lie algebras over a graded ring
Nonabelian Cohomology of Compact Lie Groups
No full textGiven a Lie group G with finitely many components and a compact Lie group A which acts on G by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map H(1)(A,K) -> H(1)(A,G) is bijective. This generalizes a classical result of Serre and a recent result of the first and third named authors of the current paper.MathematicsSCI(E)0ARTICLE2231-2361
A note on quasi-Lie and Hom-Lie structures of σ-derivations of C[z<sub>1</sub><sup>±1</sup>, \dots, z<sub>n</sub><sup>±1</sup>]
No full textIn a previous paper we studied the properties of the bracket defined by Hartwig, Larsson and the second author in (J. Algebra 295, 2006) on σ-derivations of Laurent polynomials in one variable. Here we consider the case of several variables, and emphasize on the question of when this bracket defines a hom-Lie structure rather than a quasi-Lie one.</p
[[alternative]]The study of the ocean sport’s attraction, service quality and behavioral consequences in Peng-hu
No full text[[abstract]]The main purpose of this study were to explore the relations between the ocean sport’s attraction, service quality and behavioral consequences in Peng-hu. The researcher applied the questionnaire of “the ocean sport’s attraction, service quality and behavioral consequences in Peng-hu “ and I drew 500 visitors as the research samples who participated in ocean sports in Peng-hu during August and September in 2005. The data collected from valid questionnaires were analyzed by descriptive statistics, Pearson’s product moment correlation, stepwise multiple regression analysis and canonical correlation analysis. The results are as followed:
1. The ocean sports in Peng-hu attracted visitors to a certain degree and the whole service quality is comfortable to them.
2. The relationship between the ocean sport’s attraction and service quality in Peng-hu was positive to a certain degree, and the higher service quality is, the greater ocean sport’s attraction in Peng-hu is.
3. Within each factors of the ocean sport’s attraction and the service quality, “the specialty of designing activity “and “the comfort of the environment “ had the best prediction to the loyalty of behavioral consequences; “advertisement and spread of the main activity” and “personal requirement” explain “better than any other factors.
4. The canonical correlation analysis of the study was the ocean sport’s attraction and service quality in Peng-hu have a high and positive correlation with the loyalty of behavioral consequences; the ocean sport’s attraction in Peng-hu has a moderate and positive correlation with the tendency of complaint of behavioral consequences.
Based on the results, we suggest the related organizations should:（1）strengthen the diversity of activity and develop package route of travel;（2）enforce the communication of information and promote the quality of complementary service;（3）integrate the resources and set up conservation area to build the continuous managing mold of ocean sport’s tourism.
For further research in the future: incorporate the follow-up issue of ocean sport’s tourism with profound interview and pay equal attention to qualitative research and quantitative research. Extending the subjects to related organization administrators、managers and dealers、local people and foreign tourist etc. and proceeding a comprehensive research.
楚辭 = Chu ci
No full textAnnotation of Chu Ci (Verses of Chu or Songs of Chu), which is an ancient anthology of Chinese poetry traditionally attributed mainly to Qu Yuan (c.340 BC-c.278 BC) and Song Yu (c.298 BC-c.222 BC) from the Warring States period (475 BC-221 BC)Fu "Qu Yuan lie zhuan" deng封面鐫"楚辭新註", "乾隆戊午年", "居易堂藏板"框20.8 x 14.9公分, 9行20字, 白口, 四周雙邊, 單黑魚尾. 版心上鐫"楚辭", 中鐫卷次及篇名附"屈原列傳"
楚辭 = Chu ci
No full textAnnotation of Chu Ci (Verses of Chu or Songs of Chu), which is an ancient anthology of Chinese poetry traditionally attributed mainly to Qu Yuan (c.340 BC-c.278 BC) and Song Yu (c.298 BC-c.222 BC) from the Warring States period (475 BC-221 BC)Fu "Qu Yuan lie zhuan" deng封面鐫"楚辭新註", "乾隆戊午年", "居易堂藏板"框20.8 x 14.9公分, 9行20字, 白口, 四周雙邊, 單黑魚尾. 版心上鐫"楚辭", 中鐫卷次及篇名附"屈原列傳"
Karl Heinrich Hofmann and the structure of compact groups and pro-lie groups
No full textThis article is dedicated to Karl Heinrich Hofmann on his 90th birthday. The first part of the article records some biographical facts about him. The second part focuses on the research papers and books he published with the author of this article over the last 45 years. These results concern the structure of compact groups and pro-Lie groups. © 2023 Heldermann Verlag
Space charge behavior in multi-layer oil-paper insulation under different DC voltages and temperatures
No full textOil-paper as a reliable insulation system is widely used in power transformers and cables. The dielectric properties of oil-paper insulation play an important role in the reliable operation of power equipment. However, the formation and dynamics of space charge can affect the performance of insulation material. In this paper, space charge in oil-paper insulation system has been investigated using the pulsed electroacoustic (PEA) technique. A series of measurements were carried out when the insulation system was subjected to different applied voltages at different temperatures. Charge behavior in the insulation system has been analyzed and the influence of temperature on charge dynamics was discussed. The test results show that homocharge injection takes place under all the test conditions, the applied dc voltage mainly effect the amount of space charge, while the temperature has greater influence on the distribution and mobility of space charge inside oil-paper sample
Topological Multi-groups and Multi-fields
No full textTopological groups, particularly, Lie groups are very important in differential
geometry, analytic mechanics and theoretical physics. Applying Smarandache multi-spaces, topological spaces, particularly, manifolds and groups were generalized to combinatorial manifolds and multi-groups underlying a combinatorial structure in references. Then whether can one generalizes their combination, i.e., topological group or Lie group to a multiple one? The answer is YES. In this paper, the author shows how to generalize topological groups and the homomorphism theorem for topological groups to multiple ones
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