Differential Tensor Algebras and their Module Categories
$75.99 (C)
Part of London Mathematical Society Lecture Note Series
- Authors:
- R. Bautista, National University of Mexico
- L. Salmerón, National University of Mexico
- R. Zuazua, National University of Mexico
- Date Published: October 2009
- availability: Available
- format: Paperback
- isbn: 9780521757683
$
75.99
(C)
Paperback
Other available formats:
eBook
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.
-
This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book.
Read more- Includes central results not covered in existing books
- Suitable for professional mathematicians and graduate students with only a basic knowledge of module theory
- Contains over 90 exercises for the reader to test their understanding
Reviews & endorsements
"The authors provide all minute details of every proof. The work is a remarkable example of what the reviewer would call "open source" mathematics. The reviewer feels that the publication of this important book will serve as a catalyst for further study of bocses and related structures."
Alex Martsinkovsky, Mathematical ReviewsCustomer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: October 2009
- format: Paperback
- isbn: 9780521757683
- length: 462 pages
- dimensions: 227 x 152 x 20 mm
- weight: 0.65kg
- contains: 90 exercises
- availability: Available
Table of Contents
Preface
1. t-algebras and differentials
2. Ditalgebras and modules
3. Bocses, ditalgebras and modules
4. Layered ditalgebras
5. Triangular ditalgebras
6. Exact structures in A-Mod
7. Almost split conflations in A-Mod
8. Quotient ditalgebras
9. Frames and Roiter ditalgebras
10. Product of ditalgebras
11. Hom-tensor relations and dual basis
12. Admissible modules
13. Complete admissible modules
14. Bimodule ltrations and triangular admissible modules
15. Free bimodule ltrations and free ditalgebras
16. AX is a Roiter ditalgebra, for suitable X
17. Examples and applications
18. The exact categories P(Λ), P1(Λ) and Λ-Mod
19. Passage from ditalgebras to finite dimensional algebras
20. Scalar extension and ditalgebras
21. Bimodules
22. Parametrizing bimodules and wildness
23. Nested and seminested ditalgebras
24. Critical ditalgebras
25. Reduction functors
26. Modules over non-wild ditalgebras
27. Tameness and wildness
28. Modules over non-wild ditalgebras revisited
29. Modules over non-wild algebras
30. Absolute wildness
31. Generic modules and tameness
32. Almost split sequences and tameness
33. Varieties of modules over ditalgebras
34. Ditalgebras of partially ordered sets
35. Further examples of wild ditalgebras
36. Answers to selected exercises
References
Index.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×