Operads and Universal Algebra : Proceedings of the International Conference.

Operads and Universal Algebra : Proceedings of the International Conference.

The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working...

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Bibliographic Details
Main Author: Bai, Chengming
Other Authors: Guo, Li, Loday, Jean-Louis
Format: eBook
Language:English
Published: Singapore : World Scientific, 2012.
Series:Nankai series in pure, applied mathematics and theoretical physics.
Subjects:
Operads > Congresses.
Algebra, Universal > Congresses.
Algebra, Universal
Operads
Conference papers and proceedings
Online Access:Click for online access
Table of Contents:
  • Preface; Organizing Committees; Speakers and Lectures; Participants and Photos; Contents; Grobner-Shirshov Bases for Categories L.A. Bokut, Yuqun Chen and Yu Li; 1. Introduction; 2. A short survey on Grobner-Shirshov bases; 3. Composition-Diamond lemma for categories; 3.1. Free categories and category partial algebras; 3.2. Composition-Diamond lemma for category partial algebras; 4. Grobner-Shirshov bases for the simplicial category and the cyclic category; 4.1. Grobner-Shirshov basis for the simplicial category; 4.2. Grobner-Shirshov basis for the cyclic category; References.
  • Operads, Clones, and Distributive Laws Pierre-Louis Curien1. Introduction; 2. Three useful combinators; 3. Kan extensions; 4. Kelly's account of operads; 5. Operads from analytic functors; 6. Profunctors; 7. Profunctors as a Kleisli category; 8. Distributive laws; 9. A!/Psh distributive law; 10. Intermezzo; 11. The (bi)category Prof?; 12. Cooperads and properads; References; Leibniz Superalgebras Graded by Finite Root Systems Naihong Hu, Dong Liu and Linsheng Zhu; 1. Introduction; 2. Associative super dialgebras and leibniz superalgebras; 2.1. Associative super dialgebras.
  • 2.2. Leibniz superalgebra2.3. Leibniz algebras graded by finite root systems; 3. Leibniz superalgebras graded by finite root systems; 4. The structure of the A(m, n)-graded Leibniz superalgebras (m> n); 5. The structure of -graded Leibniz superalgebras of other types; ACKNOWLEDGMENTS; References; Tridendriform Algebras Spanned by Partitions Daniel Jimenez and Maria Ronco; Introduction; 1. Preliminaries; Shuffles; 2. Rota-Baxter algebras and tridendriform bialgebras; 3. Tridendriform structure on the space of partitions; 4. Tridendriform algebra structure on the maps between finite sets.
  • 1.3.1. The Koszul complex1.3.2. The Koszul complex of the category TI with coefficients; 1.4. The category TI is Koszul; 1.5. Bibliographical remarks; 2. Comparison of three di erent types of bar constructions for an operad; 2.1. Principle of the bar construction with coefficients; 2.2. Operads as left TI-modules; 2.3. Two-sided bar construction from the free operad functor; 2.3.1. The two-sided bar construction; 2.3.2. Right TI -modules and F-functors; 2.4. The bar construction with respect to the monoidal structure.

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