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Categorification and Higher Representation Theory, Anna Beliakova, Aaron D. Lauda


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Автор: Anna Beliakova, Aaron D. Lauda
Название:  Categorification and Higher Representation Theory
ISBN: 9781470424602
Издательство: Mare Nostrum (Eurospan)
Классификация:



ISBN-10: 1470424606
Обложка/Формат: Paperback
Страницы: 363
Вес: 0.42 кг.
Дата издания: 30.03.2017
Серия: Contemporary mathematics
Язык: English
Иллюстрации: Illustrations
Размер: 254 x 178
Читательская аудитория: Professional and scholarly
Ключевые слова: Algebra,Algebraic geometry
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Поставляется из: Англии
Описание: The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory.This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory.The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.
Дополнительное описание: Algebra|Algebraic geometry


Categorification in Geometry, Topology, and Physics

Автор: Anna Beliakova, Aaron D. Lauda
Название: Categorification in Geometry, Topology, and Physics
ISBN: 1470428210 ISBN-13(EAN): 9781470428211
Издательство: Mare Nostrum (Eurospan)
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Цена: 110880.00 T
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Описание: Focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology.

Knot Invariants and Higher Representation Theory

Автор: Ben Webster
Название: Knot Invariants and Higher Representation Theory
ISBN: 1470426501 ISBN-13(EAN): 9781470426507
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ and by Mazorchuk-Stroppel and Sussan for $\mathfrak{sl}_n$.


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