Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 1: The Algebraic Theory and its Topological Background, Benoit Fresse

Автор: Benoit Fresse
Название: Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods
ISBN: 1470434822 ISBN-13(EAN): 9781470434823
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: The ultimate goal of this book is to explain that the Grothendieck-Teichmuller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck-Teichmuller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.

Автор: Hazrat
Название: Graded Rings and Graded Grothendieck Groups
ISBN: 1316619583 ISBN-13(EAN): 9781316619582
Издательство: Cambridge Academ
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Цена: 60190.00 T
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Описание: This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra, and brings together results scattered across the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

Автор: Jean-Louis Loday; Bruno Vallette
Название: Algebraic Operads
ISBN: 3642448356 ISBN-13(EAN): 9783642448355
Издательство: Springer
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Цена: 102440.00 T
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Описание: Preface.- 1.Algebras, coalgebras, homology.- 2.Twisting morphisms.- 3.Koszul duality for associative algebras.- 4.Methods to prove Koszulity of an algebra.- 5.Algebraic operad.- 6 Operadic homological algebra.- 7.Koszul duality of operads.- 8.Methods to prove Koszulity of an operad.- 9.The operads As and A\infty.- 10.Homotopy operadic algebras.- 11.Bar and cobar construction of an algebra over an operad.- 12.(Co)homology of algebras over an operad.- 13.Examples of algebraic operads.- Apendices: A.The symmetric group.- B.Categories.- C.Trees.- References.- Index.- List of Notation.

Автор: Bremner
Название: Algebraic Operads
ISBN: 1482248565 ISBN-13(EAN): 9781482248562
Издательство: Taylor&Francis
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Цена: 132710.00 T
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Описание:

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Gr bner bases in several contexts. The book builds up to the theory of Gr bner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra.

Автор: Nicola Gambino, Andre Joyal
Название: On Operads, Bimodules and Analytic Functors
ISBN: 1470425769 ISBN-13(EAN): 9781470425760
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: Develops the theory of operads and analytic functors. In particular, the authors introduce the bicategory $\operatorname{OpdBim}_{\mathcal{V}}$ of operad bimodules, that has operads as $0$-cells, operad bimodules as $1$-cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed.

Автор: Schwede, Stefan (rheinische Friedrich-wilhelms-universitat Bonn)
Название: Global homotopy theory
ISBN: 110842581X ISBN-13(EAN): 9781108425810
Издательство: Cambridge Academ
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Цена: 180570.00 T
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Описание: Global equivariant homotopy theory is presented in this self-contained book, ideal for graduate students and researchers in algebraic topology. It is a comprehensive research monograph at the forefront of current research, written by a leading expert. The book`s many examples and sample calculations make it suitable for an advanced graduate class.

Автор: Bergner, Julia E. (university Of Virginia)
Название: Homotopy theory of (гївївѕ ,1)-categories
ISBN: 1107101360 ISBN-13(EAN): 9781107101364
Издательство: Cambridge Academ
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Цена: 116160.00 T
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Описание: Homotopical or ( ,1)-categories have become a significant framework in many areas of mathematics. This book gives an introduction to the different approaches to these structures and the comparisons between them from the perspective of homotopy theory.

Автор: Bergner, Julia E. (university Of Virginia)
Название: The Homotopy theory of (?,1)-categories
ISBN: 110749902X ISBN-13(EAN): 9781107499027
Издательство: Cambridge Academ
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Цена: 40130.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Homotopical or ( ,1)-categories have become a significant framework in many areas of mathematics. This book gives an introduction to the different approaches to these structures and the comparisons between them from the perspective of homotopy theory.