9,940 research outputs found
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
Yu xu yi yan
No full textv.1. 醫林獵要 / 黃保康輯 ; [黃]任恆編校 -- v.2. 吳鞠通方歌 / 黃保康著 ; 黃任恆校注 -- 陳修園方歌 / 黃任恆編 -- v.3. 貽令堂雜俎 : [四編], 雜說, 遺詩 / 黃保康撰 ; [黃]任恆編校 -- 與壻遺言 : 附錄 / 黃保康撰.v.1. Yi lin lie yao / Huang Baokang ji ; [Huang] Renheng bian jiao -- v.2. Wu ju tong fang ge / Huang Baokang zhu ; Huang Renheng jiao zhu -- Chen Xiuyuan fang ge / Huang Renheng bian -- v.3. Yi ling tang za zu : [si bian], za shuo, yi shi / Huang Baokang zhuan ; [Huang] Renheng bian jiao -- Yu xu yi yan : fu lu / Huang Baokang zhuan.[黃保康撰].綫裝.框14.5x11.7公分, 10行20字, 小字雙行同. 黑口, 左右雙邊, 單黑魚尾. 版心中鐫題名, 卷次, 下鐫葉次.書名背頁刻"宣統三年五月刻成"《中國叢書綜錄》p.727著錄 ; 《中國中醫古籍總目》13297著錄.《貽令堂雜俎》分經, 史, 子, 集編.鈐"莊兆祥印"朱, 白文各一方.Xian zhuang.Kuang 14.5 x 11.7 gong fen, 10 hang 20 zi, xiao zi shuang hang tong. Hei kou, zuo you shuang bian, dan hei yu wei. Ban xin zhong juan ti ming, juan ci, xia juan ye ci.Shu ming bei ye ke "Xuantong san nian wu yue ke cheng"Detailed notes in vernacular field only."Yi ling tang za zu" fen jing, shi, zi, ji bian.[Huang Baokang zhuan].Qian "Zhuang Zhaoxiang yin" zhu, bai wen ge yi fang
Extensions of Self-Improving Sorters
No full textAilon et al. (SICOMP 2011) proposed a self-improving sorter that tunes its performance to the unknown input distribution in a training phase. The distribution of the input numbers x_1,x_2,...,x_n must be of the product type, that is, each x_i is drawn independently from an arbitrary distribution D_i, and the D_i's are independent of each other. We study two extensions that relax this requirement. The first extension models hidden classes in the input. We consider the case that numbers in the same class are governed by linear functions of the same hidden random parameter. The second extension considers a hidden mixture of product distributions
SALM/Lrfn Family Synaptic Adhesion Molecules
No full textSynaptic adhesion-like molecules (SALMs) are a family of cell adhesion molecules involved in regulating neuronal and synapse development that have also been implicated in diverse brain dysfunctions, including autism spectrum disorders (ASDs). SALMs, also known as leucine-rich repeat (LRR) and fibronectin III domain-containing (LRFN) proteins, were originally identified as a group of novel adhesion-like molecules that contain LRRs in the extracellular region as well as a PDZ domain-binding tail that couples to PSD-95, an abundant excitatory postsynaptic scaffolding protein. While studies over the last decade have steadily explored the basic properties and synaptic and neuronal functions of SALMs, a number of recent studies have provided novel insights into molecular, structural, functional and clinical aspects of SALMs. Here we summarize these findings and discuss how SALMs act in concert with other synaptic proteins to regulate synapse development and function
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
The classification of two step nilpotent complex Lie algebras of dimension
No full textsummary:A Lie algebra is called two step nilpotent if is not abelian and lies in the center of . Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension over the field of complex numbers. Based on the study of minimal systems of generators, we choose an appropriate basis and give a complete classification of two step nilpotent Lie algebras of dimension
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
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
Lie algebras
No full textLie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semi-simple Lie algebras and the dependence of structure of semi-simple Lie algebras on root system
Lie groups and Lie algebras
No full textThese are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT in 2020/2021.262 pages, minor corrections and improvements in v
- …
