A Polish group without Lie sums
نویسندگان
چکیده
We construct a Polish group with an invariant metric in which Lie sums and Lie brackets do not exist. The construction of the group and the proof of the main theorem use some facts of combinatorial nature about the free group with two generators equipped with a Graev metric.
منابع مشابه
A Note on Pro-lie Groups
We give a short proof of the theorem that a closed subgroup of a countable product of second countable Lie groups is pro-Lie. The point of this note is to give a short and self-contained, modulo well known results, proof of a theorem of Hofmann and Morris [3] (see also [4, Theorem 3.35] and [5]) in the case of second countable groups. Another simple proof of the result of Hofmann and Morris was...
متن کاملبررسی اثر پالیش بر روی استحکام Flexural پرسلن فلدسپاتیک و مقایسه آن با اتوگلیز و اورگلیز
Statement of Problem: Ceramic restorations are popular because they can provide the most natural replacement for teeth. However, the brittleness of ceramics is a primary disadvantage. There are various methods for strengthening ceramics such as metal framework, ceramic cores, and surface strengthening mechanisms through glazing, work hardening and ion exchange. Purpose: The purpose of this stud...
متن کاملEffect of Nail Polish on Pulse Oximetry Findings in Healthy Volunteers: A Randomized Clinical Trail
Background and Objectives: Pulse oximetry is the most common technique for monitoring hemoglobin oxygen saturation (SpO2). Different colors and brands of nail polish may cause disturbance in the reading and interpretation of oxygen saturation. The aim of this study was to determine the effect of different colors of nail polish on oxygen saturation measured by pulse oximeter. Methods: Thirty he...
متن کاملRademacher sums, Moonshine and Gravity
In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...
متن کاملSemi-direct sums of Lie algebras and discrete integrable couplings
A relation between semi-direct sums of Lie algebras and integrable couplings of lattice equations is established, and a practicable way to construct integrable couplings is further proposed. An application of the resulting general theory to the generalized Toda spectral problem yields two classes of integrable couplings for the generalized Toda hierarchy of lattice equations. The construction o...
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 2009