Corings and comodules

Lecture notes series 309

Tomasz Brzezinski, Robert Wisbauer

486 pages, parution le 22/10/2003

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Résumé

Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules.

In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry.

Coalgebras and comodules
Bialgebras and hopf algebras
Corings and comodules
Corings and extensions of rings
Corings and entwining structures
Weak corings and entwining
Appendix
Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Tomasz Brzezinski, Robert Wisbauer
Parution	22/10/2003
Nb. de pages	486
Format	15 x 22,7
Couverture	Broché
Poids	660g
Intérieur	Noir et Blanc
EAN13	9780521539319
ISBN13	978-0-521-53931-9