Methods of Graded Rings
Nastasescu, Constantin.
Methods of Graded Rings [electronic resource] / by Constantin Nastasescu, Freddy Van Oystaeyen. - XIII, 306 p. online resource. - Lecture Notes in Mathematics, 1836 0075-8434 ; . - Lecture Notes in Mathematics, 1836 .
The Category of Graded Rings -- The Category of Graded Modules -- Modules over Stronly Graded Rings -- Graded Clifford Theory -- Internal Homogenization -- External Homogenization -- Smash Products -- Localization of Graded Rings -- Application to Gradability -- Appendix A: Some Category Theory -- Appendix B: Dimensions in an Abelian Category -- Bibliography -- Index.
The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.
9783540409984
10.1007/b94904 doi
Algebra.
Group theory.
Mathematical physics.
Algebra.
Associative Rings and Algebras.
Category Theory, Homological Algebra.
Group Theory and Generalizations.
Mathematical Methods in Physics.
QA150-272
512
Methods of Graded Rings [electronic resource] / by Constantin Nastasescu, Freddy Van Oystaeyen. - XIII, 306 p. online resource. - Lecture Notes in Mathematics, 1836 0075-8434 ; . - Lecture Notes in Mathematics, 1836 .
The Category of Graded Rings -- The Category of Graded Modules -- Modules over Stronly Graded Rings -- Graded Clifford Theory -- Internal Homogenization -- External Homogenization -- Smash Products -- Localization of Graded Rings -- Application to Gradability -- Appendix A: Some Category Theory -- Appendix B: Dimensions in an Abelian Category -- Bibliography -- Index.
The topic of this book, graded algebra, has developed in the past decade to a vast subject with new applications in noncommutative geometry and physics. Classical aspects relating to group actions and gradings have been complemented by new insights stemming from Hopf algebra theory. Old and new methods are presented in full detail and in a self-contained way. Graduate students as well as researchers in algebra, geometry, will find in this book a useful toolbox. Exercises, with hints for solution, provide a direct link to recent research publications. The book is suitable for courses on Master level or textbook for seminars.
9783540409984
10.1007/b94904 doi
Algebra.
Group theory.
Mathematical physics.
Algebra.
Associative Rings and Algebras.
Category Theory, Homological Algebra.
Group Theory and Generalizations.
Mathematical Methods in Physics.
QA150-272
512