Reduction of τ-tilting modules and torsion pairs
(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)
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- author
- Jasso, Gustavo LU
- publishing date
- 2015
- 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
- 2023-03-08 09:48:29
@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}}, }