Differential Tensor Algebras and their Module Categories
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Differential Tensor Algebras and their Module Categories

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eBook - PDF

Differential Tensor Algebras and their Module Categories

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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.

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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

Publisher
Cambridge University Press
Year
2009
ISBN
9781139118958
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

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