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http://hdl.handle.net/1942/25368
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DC Field | Value | Language |
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dc.contributor.author | WANG, Zhihua | - |
dc.contributor.author | Li, Libin | - |
dc.contributor.author | ZHANG, Yinhuo | - |
dc.date.accessioned | 2017-12-22T14:38:26Z | - |
dc.date.available | 2017-12-22T14:38:26Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | GLASGOW MATHEMATICAL JOURNAL, 60(1), p. 253-272 | - |
dc.identifier.issn | 0017-0895 | - |
dc.identifier.uri | http://hdl.handle.net/1942/25368 | - |
dc.description.abstract | This paper deals with the Green ring G(C) of a finite tensor category C with finitely many indecomposable objects over an algebraically closed field k. The first part of this paper is through the Casimir number of C to determine when the Green ring G(C), or the Green algebra G(C)⊗Z K over a field K is Jacobson semisimple (namely, has zero Jacobson radical). It turns out that G(C) ⊗Z K is Jacobson semisimple if and only if the Casimir number of C is not zero in K. For the Green ring G(C) itself, G(C) is Jacobson semisimple if and only if the Casimir number of C is not zero. The second part of this paper focuses on the case where C = Rep(kG) for a cyclic group G of order p over a field k of characteristic p. In this case, the Casimir number of C is computable and is shown to be 2p 2. This leads to a complete description of the Jacobson radical of the Green algebra G(C) ⊗Z K over any field K. | - |
dc.description.sponsorship | The first author was funded by China Postdoctoral Science Foundation (Grant No. 2017M610316), the second author was funded by the NSF of China (Grant No. 11471282). | - |
dc.language.iso | en | - |
dc.rights | Glasgow Mathematical Journal Trust 2017. | - |
dc.subject.other | finite tensor category; green ring; Casimir number, Jacobson radical, Frobenius algebra. | - |
dc.title | A criterion for the Jacobson semisimplicity of the green ring of a finite tensor category | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 272 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 253 | - |
dc.identifier.volume | 60 | - |
local.bibliographicCitation.jcat | A1 | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1017/S0017089517000246 | - |
dc.identifier.isi | 000417506500019 | - |
item.fullcitation | WANG, Zhihua; Li, Libin & ZHANG, Yinhuo (2018) A criterion for the Jacobson semisimplicity of the green ring of a finite tensor category. In: GLASGOW MATHEMATICAL JOURNAL, 60(1), p. 253-272. | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2019 | - |
item.contributor | WANG, Zhihua | - |
item.contributor | Li, Libin | - |
item.contributor | ZHANG, Yinhuo | - |
item.accessRights | Open Access | - |
crisitem.journal.issn | 0017-0895 | - |
crisitem.journal.eissn | 1469-509X | - |
Appears in Collections: | Research publications |
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criterion_for_the_jacobson_semisimplicity_of_the_green_ring_of_a_finite_tensor_category.pdf Restricted Access | Published version | 189.34 kB | Adobe PDF | View/Open Request a copy |
semisimplicity-of-Green-rings-7.pdf | Peer-reviewed author version | 405.41 kB | Adobe PDF | View/Open |
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