Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Loday J.-L., Vallette B. — Algebraic Operads. Version 0.99
Loday J.-L., Vallette B. — Algebraic Operads. Version 0.99

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Algebraic Operads. Version 0.99

Авторы: Loday J.-L., Vallette B.

Аннотация:

An operad is an algebraic device, which encodes a type of algebras. Instead of studying the properties of a particular algebra, we focus on the universal operations that can be performed on the elements of any algebra of a given type. The information contained in an operad consists in these operations and all the ways of composing them. The classical types of algebras, that is associative algebras, commutative algebras and Lie algebras, give first examples of algebraic operads. Recently, there has been much interest in other types of algebras, to name a few: Poisson algebras, Gerstenhaber algebras, Jordan algebras, pre-Lie algebras, Batalin-Vilkovisky alge- bras, Leibniz algebras, dendriform algebras and the various types of algebras up to homotopy. The notion of operad permits us to study them conceptually and to compare them. The operadic point of view has several advantages. First, many results known for classical algebras, when written in the operadic language, allows us to apply them to other types of algebras. Second, the operadic language simplifies both the statements and the proofs. So, it clarifies the global understanding and allows one to go further. Third, even for classical algebras, the operad theory provides new results that had not been unraveled before. Operadic theorems have been applied to prove results in other fields, like the deformation-quantization of Poisson manifolds by Maxim Kontsevich and Dmitry Tamarkin for instance. Nowadays, operads appear in many different themes: algebraic topology, differential geometry, noncommutative geometry, C ∗ -algebras, symplectic geometry, deformation theory, quantum field theory, string topology, renormalization theory, combinatorial algebra, category theory, universal algebra and computer science.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 2010

Количество страниц: 530

Добавлена в каталог: 08.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте