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The D-standard and K-standard categories
- Source :
- Advances in Mathematics. 333:159-193
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- We introduce the notions of a $\mathbf{D}$-standard abelian category and a $\mathbf{K}$-standard additive category. We prove that for a finite dimensional algebra $A$, its module category is $\mathbf{D}$-standard if and only if any derived autoequivalence on $A$ is standard, that is, given by a two-sided tilting complex. We prove that if the subcategory of projective $A$-modules is $\mathbf{K}$-standard, then the module category is $\mathbf{D}$-standard. We provide new examples of $\mathbf{D}$-standard module categories.<br />revised, comments are welcome
- Subjects :
- Additive category
Subcategory
Pure mathematics
Functor
General Mathematics
010102 general mathematics
05 social sciences
K-Theory and Homology (math.KT)
Mathematics - Rings and Algebras
01 natural sciences
Rings and Algebras (math.RA)
If and only if
Mathematics::Category Theory
Tensor (intrinsic definition)
Mathematics - K-Theory and Homology
0502 economics and business
FOS: Mathematics
Abelian category
Representation Theory (math.RT)
050207 economics
0101 mathematics
Projective test
Algebra over a field
Mathematics - Representation Theory
Mathematics
Subjects
Details
- ISSN :
- 00018708
- Volume :
- 333
- Database :
- OpenAIRE
- Journal :
- Advances in Mathematics
- Accession number :
- edsair.doi.dedup.....5d433a687aa7a66ec293d8882277c1a5