The Conjugacy Theorems
نویسنده
چکیده
We use the theory of differential forms, orientation, and mapping degree to prove that all maximal tori in a compact connected Lie group are conjugate. We also prove that all Lie groups are orientable, and that if G is a compact connected Lie group and T a maximal torus of G, then dim G/T is even.
منابع مشابه
Central and Local Limit Theorems for Excedances by Conjugacy Class and by Derangement
We give central and local limit theorems for the number of excedances of a uniformly distributed random permutation belonging to certain sequences of conjugacy classes and belonging to the sequence of derangements.
متن کاملCommuting conjugacy classes: An application of Hall’s Marriage Theorem to Group Theory
Let G be a finite group. Define a relation ∼ on the conjugacy classes of G by setting C ∼ D if there are representatives c ∈ C and d ∈ D such that cd = dc. In the case where G has a normal subgroup H such that G/H is cyclic, two theorems are proved concerning the distribution, between cosets of H, of pairs of conjugacy classes of G related by ∼. One of the proofs involves an interesting applica...
متن کاملMTS 311 COURSE TITLE - Groups and Rings
COURSE CONTENT: Groups, Examples of groups, Some elementary properties of groups, Subgroups, Cyclic groups, Cosets and Langrange’s theorem, Normal subgroups and Quotient groups, Homomorphisms, The Isomorphism Theorems, Group Actions, orbits and stabilizers, Conjugacy, Class equation of a finite group, Cauchy’s Theorem, The structure of p-groups, The Sylow’s theorems, Some applications of Sylow’...
متن کاملThe Structure of Conjugacy Closed Loops
We study structure theorems for the conjugacy closed (CC-) loops, a specific variety of G-loops (loops isomorphic to all their loop isotopes). These theorems give a description all such loops of small order. For example, if p and q are primes, p < q, and q − 1 is not divisible by p, then the only CC-loop of order pq is the cyclic group of order pq. For any prime q > 2, there is exactly one non-...
متن کاملEssential Dimension of Involutions and Subalgebras
We use theorems of N. Karpenko about the incompressibility of Severi Brauer varieties and quadratic Weil transfers of Severi Brauer varieties to compute the minimal number of parameters needed to define conjugacy classes of involutions of given type on division algebras of 2-primary index. Similarly we compute the minimal number of parameters needed to define conjugacy classes of étale subalgeb...
متن کاملGeneration of Conjugate Directions for Unconstrained Minimization without Derivatives
We analyze a technique for unconstrained minimization without derivatives. This stems from two theorems proved by M. J. D. Powell. A particular version, which we consider in detail, is related to the Jacobi process for finding the eigensystem of a symmetric matrix, and the two processes, although different, help to illuminate one another. We study convergence of the search directions to mutual ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008