Rota-Baxter 代数导论

出版社:高等教育出版社
出版日期:2012-8
ISBN:9787040348248
作者:郭锂
页数:226页

书籍目录

Preface
Leitfaden
Part I The Operator Aspect of Rota-Baxter Algebra
1 Spitzer's Identity
1.1 Basic definitions, examples and properties
1.2 Complete Rota-Baxter algebras
1.3 Formulations of Spitzer's identity, old and new
1.4 Atkinson's multiplicative decomposition and the algebraic
Bogoliubov map
1.5 Some related literature and problems
2 Connected Hopf Algebras and Rota-Baxter Algebras
2.1 Algebras and modules revisited
2.2 Coalgebras and bialgebras
2.3 Connected bialgebra and Hopf algebra
2.4 Algebraic Birkhoff decomposition
2.5 Some related literature and problems
Part II The Structure Aspect of Rota-Baxter Algebra
3 Free Commutative Rota-Baxter Algebras and Shuffle
Products
3.1 Shuffle product and generalizations
3.2 Free commutative Rota-Baxter algebras
3.3 Rota-Baxter algebras, Stirling numbers and partitions
3.4 Some related literature and problems
4 Free Noncommutative Rota-Baxter Algebras and Rooted Trees
4.1 The Rota-Baxter algebra of trees
4.2 Free Rota-Baxter algebra on a set
4.3 Unitarization of Rota-Baxter algebras
4.4 Free Rota-Baxter algebra on an algebra
4.5 Some related literature and problems
Part III The Operad Aspect of Rota-Baxter Algebra
5 Rota-Baxter Algebras and Dendriform Algebras
5.1 Concepts and basic properties
5.2 Free objects in the commutative case and shuffle products
5.3 Universal enveloping algebras of tridendriform algebras
5.4 Free dendriform, tridendriform algebras and free
Rota-Baxter algebras
5.5 Some related literature and problems
6 Rota-Baxter Operators on Operads and Manin Products
6.1 Nonsymmetric operads
6.2 Products of binary quadratic NS operads
6.3 Binary quadratic ns operads from linear operators
6.4 Some related literature and problems
Bibliography
Index

作者简介

《Rot-Baxter代数导论(英文版)》是第—本介绍该领域的著作,通过大量的例子以及各种应用之间的联系,详细介绍了Rota—Baxter代数,包括它的三个重要方面。Rota—Baxter代数由一个结合代数和一个线性算子组成,该算子满足微积分的分部积分公式中的等式。Rota—Baxter代数20世纪60年代起源于随机理论。本世纪以来,Rota—Baxter代数不仅在理论法方面得到了突飞猛进的发展,并且在数学物理、数论、组合等方面得到了广泛的应用。

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