Rota-Baxter代數導論（英文版）簡(jiǎn)介，目錄書(shū)摘
2019-10-15 17:23
來(lái)源：京東
作者：京東
Rota-Baxter代數導論（英文版）
暫無(wú)報價(jià)
400+評論
97%好評
內容簡(jiǎn)介: Rota-Baxter代數由一個(gè)結合代數和一個(gè)線(xiàn)性算子組成，該算子滿(mǎn)足微積分的分部積分公式中的等式。Rota-Baxter代數20世紀60年代起源于隨機理論。本世紀以來(lái)，Rota-Baxter代數不僅在理論法方面得到了突飛猛進(jìn)的發(fā)展，并且在數學(xué)物理、數論、組合等方面得到了廣泛的應用。盡管過(guò)去的幾十年有很多有關(guān)于Rota-Baxter代數的文章，但是還缺乏一本系統介紹Rota-Baxter代數的專(zhuān)著(zhù)?！禦ota-Baxter代數導論（英文版）》就是介紹該領(lǐng)域的著(zhù)作，通過(guò)大量的例子以及各種應用之間的聯(lián)系，詳細介紹了Rota-Baxter代數，包括它的三個(gè)重要方面。
本書(shū)可作為代數、組合、數論和數學(xué)物理領(lǐng)域的研究生教材或參考書(shū)，也可供相關(guān)的研究人員參考。
作者郭鋰為美國Rutgers大學(xué)教授，是Rota-Baxter代數及相關(guān)結構近年來(lái)進(jìn)展的主要貢獻者之一。郭鋰教授在Notices of the American Mathematical Society發(fā)表的文章WHAT IS a Rota-Baxter Algebra將這個(gè)新的研究領(lǐng)域帶入了數學(xué)公眾的視野。
本書(shū)可作為代數、組合、數論和數學(xué)物理領(lǐng)域的研究生教材或參考書(shū)，也可供相關(guān)的研究人員參考。
作者郭鋰為美國Rutgers大學(xué)教授，是Rota-Baxter代數及相關(guān)結構近年來(lái)進(jìn)展的主要貢獻者之一。郭鋰教授在Notices of the American Mathematical Society發(fā)表的文章WHAT IS a Rota-Baxter Algebra將這個(gè)新的研究領(lǐng)域帶入了數學(xué)公眾的視野。
作者簡(jiǎn)介:
目錄: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
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
京公網(wǎng)安備 11000002000088號
