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Lie methods in deformation theory

Manetti, Marco.

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Lie methods in deformation theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lie methods in deformation theory/ by Marco Manetti.
Author:	Manetti, Marco.
Published:	Singapore :Springer Nature Singapore : : 2022.,
Description:	xii, 574 p. :ill., digital ;24 cm.
[NT 15003449]:	1. An Overview of Deformation Theory of Complex Manifolds -- 2. Lie Algebras -- 3. Functors of Artin Rings -- 4. Infinitesimal Deformations of Complex Manifolds and Vector Bundles -- 5. Differential Graded Lie Algebras -- 6. Maurer-Cartan Equation and Deligne Groupoids -- 7. Totalization and Descent of Deligne Groupoids -- 8. Deformations of Complex Manifolds and Holomorphic Maps -- 9. Poisson, Gerstenhaber and Batalin-Vilkovisky Algebras -- 10. L1-algebras -- 11. Coalgebras and Coderivations -- 12. L1-morphisms -- 13. Formal Kuranishi Families and Period Maps -- References.
Contained By:	Springer Nature eBook
Subject:	Lie algebras. -
Online resource:	https://doi.org/10.1007/978-981-19-1185-9
ISBN:	9789811911859

Lie methods in deformation theory
Manetti, Marco.

Lie methods in deformation theory[electronic resource] /by Marco Manetti. - Singapore :Springer Nature Singapore :2022. - xii, 574 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

1. An Overview of Deformation Theory of Complex Manifolds -- 2. Lie Algebras -- 3. Functors of Artin Rings -- 4. Infinitesimal Deformations of Complex Manifolds and Vector Bundles -- 5. Differential Graded Lie Algebras -- 6. Maurer-Cartan Equation and Deligne Groupoids -- 7. Totalization and Descent of Deligne Groupoids -- 8. Deformations of Complex Manifolds and Holomorphic Maps -- 9. Poisson, Gerstenhaber and Batalin-Vilkovisky Algebras -- 10. L1-algebras -- 11. Coalgebras and Coderivations -- 12. L1-morphisms -- 13. Formal Kuranishi Families and Period Maps -- References.

This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer-Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

ISBN: 9789811911859

Standard No.: 10.1007/978-981-19-1185-9doiSubjects--Topical Terms:

526115
Lie algebras.

LC Class. No.: QA252.3 / .M35 2022

Dewey Class. No.: 512.482

Lie methods in deformation theory
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100 1 $a Manetti, Marco. $3 901342
245 1 0 $a Lie methods in deformation theory $h [electronic resource] / $c by Marco Manetti.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2022.
300 $a xii, 574 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a 1. An Overview of Deformation Theory of Complex Manifolds -- 2. Lie Algebras -- 3. Functors of Artin Rings -- 4. Infinitesimal Deformations of Complex Manifolds and Vector Bundles -- 5. Differential Graded Lie Algebras -- 6. Maurer-Cartan Equation and Deligne Groupoids -- 7. Totalization and Descent of Deligne Groupoids -- 8. Deformations of Complex Manifolds and Holomorphic Maps -- 9. Poisson, Gerstenhaber and Batalin-Vilkovisky Algebras -- 10. L1-algebras -- 11. Coalgebras and Coderivations -- 12. L1-morphisms -- 13. Formal Kuranishi Families and Period Maps -- References.
520 $a This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer-Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
650 0 $a Lie algebras. $3 526115
650 1 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Commutative Rings and Algebras. $3 891076
650 2 4 $a Differential Geometry. $3 891003
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-981-19-1185-9
950 $a Mathematics and Statistics (SpringerNature-11649)