Differential Tensor Algebras and their Module Categories
eBook - PDF

Differential Tensor Algebras and their Module Categories

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Differential Tensor Algebras and their Module Categories

About this book

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.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Differential Tensor Algebras and their Module Categories by R. Bautista,L. Salmerón,R. Zuazua in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. 1 t-algebras and differentials
  7. 2 Ditalgebras and modules
  8. 3 Bocses, ditalgebras and modules
  9. 4 Layered ditalgebras
  10. 5 Triangular ditalgebras
  11. 6 Exact structures in A-Mod
  12. 7 Almost split conflations in A-Mod
  13. 8 Quotient ditalgebras
  14. 9 Frames and Roiter ditalgebras
  15. 10 Product of ditalgebras
  16. 11 Hom-tensor relations and dual basis
  17. 12 Admissible modules
  18. 13 Complete admissible modules
  19. 14 Bimodule filtrations
  20. 15 Free bimodule filtrations and free ditalgebras
  21. 16 AX is a Roiter ditalgebra, for suitable X
  22. 17 Examples and applications
  23. 18 The exact categories P(Λ), P1(Λ) and Λ - Mod
  24. 19 Passage from ditalgebras
  25. 20 Scalar extension and ditalgebras
  26. 21 Bimodules
  27. 22 Parametrizing bimodules and wildness
  28. 23 Nested and seminested ditalgebras
  29. 24 Critical ditalgebras
  30. 25 Reduction functors
  31. 26 Modules over non-wild ditalgebras
  32. 27 Tameness and wildness
  33. 28 Modules over non-wild ditalgebras revisited
  34. 29 Modules over non-wild algebras
  35. 30 Absolute wildness
  36. 31 Generic modules and tameness
  37. 32 Almost split sequences and tameness
  38. 33 Varieties of modules over ditalgebras
  39. 34 Ditalgebras of partially ordered sets
  40. 35 Further examples of wild ditalgebras
  41. 36 Answers to selected exercises
  42. References
  43. Index