Differential tensor algebras and their module categories [E-Book] / R. Bautista, L. Salmerón, and R. Zuazua.
Bautista, R., (author)
Salmerón, L., (author) / Zuazua, R., (author)
Cambridge : Cambridge University Press, 2009
1 online resource (ix, 452 pages)
englisch
9781139107105
9780521757683
London Mathematical Society lecture note series ; 362
Full Text
Table of Contents:
  • T-algebras and differentials
  • Dutalgebras and modules
  • Bocses, ditalgebras and modules
  • Layered ditalgebras
  • Exact structures in A-mod
  • Quotient ditalgebras
  • Frames and roiter ditalgebras
  • Product of ditalgebras
  • Hom-tensor relations and dual basis
  • Admissible modules
  • Complete admissible modules
  • Bimodule filtrations and triangular admissible modules
  • Free bimodule filtrations and free datalgebras
  • Examples and applications
  • Passage from ditalgebras to finite-dimensional algebras
  • Scalar extension and ditalgebras
  • Bimodules
  • Parametrizing bimodules and wildness
  • Nested and seminested ditalgebras
  • Critical diatalgebras
  • Critical ditalgebras
  • Reduction functors
  • Reduction functions
  • Modules over non-wild ditalgebras
  • Tameness and wildness
  • Modules over non-wild ditalgebras revisited
  • Modules over non-wild algebras
  • Absolute wildness
  • Generic modules and tameness
  • Varieties of modules over ditalgebras
  • Ditalgebras of partially ordered sets
  • Further examples of wild ditalgebras
  • Answers to selected exercises.