Squared Hopf algebras / Volodymyr V. Lyubashenko.

Format:

Book

Author/Creator:

Lyubashenko, Volodymyr V., 1959- author.

Series:

Memoirs of the American Mathematical Society ; no. 677.

Memoirs of the American Mathematical Society, 0065-9266 ; number 677

Language:

English

Subjects (All):

Hopf algebras.

Physical Description:

1 online resource (197 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1999]

Language Note:

English

Summary:

This book is intended for graduate students and research mathematicians interested in associative rings and algebras.

Contents:

""Contents""; ""Introduction""; ""Chapter 1. Tools""; ""1.1. Tensor product of abelian categories""; ""1.2. Monoidal categories""; ""1.3. Monoidal abelian categories""; ""1.4. Symmetric monoidal 2-category of abelian categories""; ""1.5. System of notations""; ""1.6. Monoidal structures on V [omitted] V""; ""1.7. Ind-objects""; ""1.8. Rigid-abelian categories""; ""Chapter 2. Squared coalgebras""; ""2.1. Definitions""; ""2.2. Comodules""; ""2.3. The fundamental theorem on coalgebras""; ""2.4. Relationship between categories of comodules""; ""2.5. The category of fibre functors""

""2.6. Reconstruction theorems""""2.7. Comodules over ordinary coalgebras""; ""2.8. Construction data""; ""Chapter 3. Squared bicoalgebras""; ""3.1. Tensor product of squared coalgebras""; ""3.2. Bicoalgebras""; ""3.3. Monoidal construction data""; ""3.4. Tensor generators and relations""; ""3.5. Relationship with braided bialgebras""; ""3.6. Commutative algebras and braiding""; ""Chapter 4. Hopf coalgebras""; ""4.1. Opposite coalgebras""; ""4.2. Comparison with opposite coalgebra in braided case""; ""4.3. The antipode""; ""4.4. Comparison with braided Hopf algebras""

""4.5. Multiplication in the opposite bialgebra""""4.6. Reconstruction of rigid monoidal categories""; ""Chapter 5. Quasitriangular Hopf coalgebras""; ""5.1. R-matrices in Hopf coalgebras""; ""5.2. Braiding for comodules over a braided Hopf algebra""; ""5.3. Constructing braided categories""; ""5.4. Ribbon Hopf coalgebras""; ""5.5. Ribbon reconstruction""; ""Appendix A. Symmetric monoidal 2-categories""; ""A.1. A review of 2-categories""; ""A.2. 2-pasting schemes""; ""A.3. Weak 2-pasting""; ""A.4. Weak 3-categories""; ""A.5. A monoidal 2-category of abelian categories""

""A.6. Symmetric monoidal 2-categories""""A.7. A symmetric monoidal 2-category of abelian categories""; ""Bibliography""

Notes:

"November 1999, volume 142, number 677 (third of 4 numbers)."

Includes bibliographical references (pages 179-180).

Description based on print version record.

ISBN:

1-4704-0268-8