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Reduction of τ-tilting modules and torsion pairs

Jasso, Gustavo LU (2015) In International Mathematics Research Notices 2015(16). p.7190-7237
Abstract
The class of support τ -tilting modules was introduced recently by Adachi et al. These
modules complete the class of tilting modules from the point of view of mutations. Given
a finite-dimensional algebra A, we study all basic support τ -tilting A-modules which
have a given basic τ -rigid A-module as a direct summand. We show that there exist an
algebra C such that there exists an order-preserving bijection between these modules
and all basic support τ -tilting C-modules; we call this passage τ -tilting reduction. An
important step in our proof is the formation of τ -perpendicular categories which are
analogs of ordinary perpendicular categories. Finally, we show that τ -tilting reduction
is compatible with... (More)
The class of support τ -tilting modules was introduced recently by Adachi et al. These
modules complete the class of tilting modules from the point of view of mutations. Given
a finite-dimensional algebra A, we study all basic support τ -tilting A-modules which
have a given basic τ -rigid A-module as a direct summand. We show that there exist an
algebra C such that there exists an order-preserving bijection between these modules
and all basic support τ -tilting C-modules; we call this passage τ -tilting reduction. An
important step in our proof is the formation of τ -perpendicular categories which are
analogs of ordinary perpendicular categories. Finally, we show that τ -tilting reduction
is compatible with silting reduction and 2-Calabi–Yau reduction in appropriate triangulated categories. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2015
issue
16
pages
48 pages
publisher
Oxford University Press
external identifiers
  • scopus:84954245483
ISSN
1073-7928
DOI
10.1093/imrn/rnu163
language
English
LU publication?
no
id
b5a232a3-b3e4-489a-b1e0-31b20c892fba
date added to LUP
2022-03-09 15:17:03
date last changed
2025-10-14 12:53:38
@article{b5a232a3-b3e4-489a-b1e0-31b20c892fba,
  abstract     = {{The class of support τ -tilting modules was introduced recently by Adachi et al. These<br>
modules complete the class of tilting modules from the point of view of mutations. Given<br>
a finite-dimensional algebra A, we study all basic support τ -tilting A-modules which<br>
have a given basic τ -rigid A-module as a direct summand. We show that there exist an<br>
algebra C such that there exists an order-preserving bijection between these modules<br>
and all basic support τ -tilting C-modules; we call this passage τ -tilting reduction. An<br>
important step in our proof is the formation of τ -perpendicular categories which are<br>
analogs of ordinary perpendicular categories. Finally, we show that τ -tilting reduction<br>
is compatible with silting reduction and 2-Calabi–Yau reduction in appropriate triangulated categories.}},
  author       = {{Jasso, Gustavo}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  number       = {{16}},
  pages        = {{7190--7237}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Reduction of τ-tilting modules and torsion pairs}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnu163}},
  doi          = {{10.1093/imrn/rnu163}},
  volume       = {{2015}},
  year         = {{2015}},
}