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http://hdl.handle.net/1942/31932
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DC Field | Value | Language |
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dc.contributor.author | Chen, Huixiang | - |
dc.contributor.author | ZHANG, Yinhuo | - |
dc.date.accessioned | 2020-09-17T13:48:04Z | - |
dc.date.available | 2020-09-17T13:48:04Z | - |
dc.date.issued | 2020 | - |
dc.date.submitted | 2020-09-12T12:21:30Z | - |
dc.identifier.citation | Bulletin of the Belgian Mathematical Society Simon Stevin (Printed), 27 (2) , p. 245 -279 | - |
dc.identifier.issn | 1370-1444 | - |
dc.identifier.uri | http://hdl.handle.net/1942/31932 | - |
dc.description.abstract | In this paper, we study tensor (or monoidal) categories of finite rank over an algebraically closed field F. Given a tensor category C, we have two structure invariants of C: the Green ring (or the representation ring) r(C) and the Auslander algebra A(C) of C. We show that a Krull-Schmit abelian tensor category C of finite rank is uniquely determined (up to tensor equivalences) by its two structure invariants and the associated associator system of C. In fact, we can reconstruct the tensor category C from its two invariants and the associator system. More general, given a quadruple (R, A, φ, a) satisfying certain conditions, where R is a Z+-ring of rank n, A is a finite dimensional F-algebra with a complete set of n primitive orthogonal idempotents, φ is an algebra map from A ⊗F A to an algebra M(R, A) constructed from A and R, and a = {ai,j,l |1 6 i, j, l 6 n} is a family of “invertible” matrices over A, we can construct a Krull-Schmidt and abelian tensor category C over F such that R is the Green ring of C and A is the Auslander algebra of C. In this case, C has finitely many indecomposable objects (up to isomorphisms) and finite dimensional Hom-spaces. Moreover, we will give a necessary and sufficient condition for such two tensor categories to be tensor equivalent. | - |
dc.description.sponsorship | We thank FWO and BOF of UHasselt for their financial support. The first author is also supported by NSFC (Grant No.11571298, 11711530703). The second author is financed by FWO (N1518617). | - |
dc.language.iso | en | - |
dc.publisher | BELGIAN MATHEMATICAL SOC TRIOMPHE | - |
dc.rights | 2020 Project Euclid. | - |
dc.subject.other | Green ring | - |
dc.subject.other | Auslander algebra | - |
dc.subject.other | associator | - |
dc.subject.other | tensor category | - |
dc.title | Reconstruction of tensor categories from their structure invariants | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 279 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 245 | - |
dc.identifier.volume | 27 | - |
local.format.pages | 35 | - |
local.bibliographicCitation.jcat | A1 | - |
local.publisher.place | CP 218,01 BOULEVARD TRIOMPE, B 1050 BRUSSELS, BELGIUM | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.isi | WOS:000549353400005 | - |
dc.identifier.url | https://projecteuclid.org/euclid.bbms/1594346417 | - |
dc.identifier.eissn | 2034-1970 | - |
local.provider.type | - | |
local.uhasselt.uhpub | yes | - |
item.fullcitation | Chen, Huixiang & ZHANG, Yinhuo (2020) Reconstruction of tensor categories from their structure invariants. In: Bulletin of the Belgian Mathematical Society Simon Stevin (Printed), 27 (2) , p. 245 -279. | - |
item.accessRights | Closed Access | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2021 | - |
item.contributor | Chen, Huixiang | - |
item.contributor | ZHANG, Yinhuo | - |
crisitem.journal.issn | 1370-1444 | - |
crisitem.journal.eissn | 2034-1970 | - |
Appears in Collections: | Research publications |
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