| 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 |
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