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On standard derived equivalences of orbit categories
| Content Provider | Semantic Scholar |
|---|---|
| Author | Volkov, Y. V. Zvonareva, Alexandra |
| Copyright Year | 2015 |
| Abstract | Let k be a commutative ring, A and B – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kb pB to K b pA. We construct a map from the set of standard G-equivalences to the set of standard equivalences from Kb pB to K b pA and a map from the set of standard G-equivalences from Kb pB to K b pA to the set of standard equivalences from K b p(B/G) to K b p(A/G). We investigate the properties of these maps and apply our results to the case where A = B = R is a Frobenius k-algebra and G is the cyclic group generated by its Nakayama automorphism ν. We apply this technique to obtain the generating set of the derived Picard group of a Frobenius Nakayama algebra over an algebraically closed field. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://export.arxiv.org/pdf/1501.00709 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Categories Graph automorphism Map Matrix multiplication MusicBrainz Picard Turing completeness |
| Content Type | Text |
| Resource Type | Article |
