ota—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。尽管过 去的几十年有很多有关于rota-baxter代数的文章，但是还缺乏一本系统介绍rota-baxter代数的专著。本书就是第一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 代数导论 (英文版)》可作为代数、组合、数论和数学物理领域的研究生教材或参考书，也可供相关的研究人员参考。
作者郭锂为美国rutgers大学教授，是rota-baxter代数及相关结构近年来进展的主要贡献者之一。郭锂教授在notices of the american mathematical sociefy发表的文章what is a rota—baxter algebra将这个新的研究领域带入了数学公众的视野。
- 前辅文
- 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
