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Rota-Baxter代数导论 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Rota-Baxter代数导论 英文
  • 郭锂著 著
  • 出版社： 北京：高等教育出版社
  • ISBN：7040348248
  • 出版时间：2012
  • 标注页数：226页
  • 文件大小：33MB
  • 文件页数：239页
  • 主题词：

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图书目录

Part Ⅰ The Operator Aspect of Rota-Baxter Algebra3

1 Spitzer's Identity3

1.1 Basic definitions,examples and properties4

1.2 Complete Rota-Baxter algebras19

1.3 Formulations of Spitzer's identity,old and new22

1.4 Atkinson's multiplicative decomposition and the algebraic Bogoliubov map39

1.5 Some related literature and problems43

2 Connected Hopf Algebras and Rota-Baxter Algebras47

2.1 Algebras and modules revisited48

2.2 Coalgebras and bialgebras50

2.3 Connected bialgebra and Hopf algebra54

2.4 Algebraic Birkhoff decomposition62

2.5 Some related literature and problems69

Part Ⅱ The Structure Aspect of Rota-Baxter Algebra73

3 Free Commutative Rota-Baxter Algebras and Shuffle Products73

3.1 Shuffle product and generalizations74

3.2 Free commutative Rota-Baxter algebras92

3.3 Rota-Baxter algebras,Stirling numbers and partitions107

3.4 Some related literature and problems116

4 Free Noncommutative Rota-Baxter Algebras and Rooted Trees119

4.1 The Rota-Baxter algebra of trees120

4.2 Free Rota-Baxter algebra on a set128

4.3 Unitarization of Rota-Baxter algebras147

4.4 Free Rota-Baxter algebra on an algebra151

4.5 Some related literature and problems163

Part Ⅲ The Operad Aspect of Rota-Baxter Algebra167

5 Rota-Baxter Algebras and Dendriform Algebras167

5.1 Concepts and basic properties168

5.2 Free objects in the commutative case and shuffle products171

5.3 Universal enveloping algebras of tridendriform algebras177

5.4 Free dendriform,tridendriform algebras and free Rota-Baxter algebras180

5.5 Some related literature and problems190

6 Rota-Baxter Operators on Operads and Manin Products191

6.1 Nonsymmetric operads192

6.2 Products of binary quadratic NS operads196

6.3 Binary quadratic ns operads from linear operators204

6.4 Some related literature and problems209

Bibliography211

Index223

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