Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/25368
Title: | A criterion for the Jacobson semisimplicity of the green ring of a finite tensor category | Authors: | WANG, Zhihua Li, Libin ZHANG, Yinhuo |
Issue Date: | 2018 | Source: | GLASGOW MATHEMATICAL JOURNAL, 60(1), p. 253-272 | 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. | Keywords: | finite tensor category; green ring; Casimir number, Jacobson radical, Frobenius algebra. | Document URI: | http://hdl.handle.net/1942/25368 | ISSN: | 0017-0895 | e-ISSN: | 1469-509X | DOI: | 10.1017/S0017089517000246 | ISI #: | 000417506500019 | Rights: | Glasgow Mathematical Journal Trust 2017. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
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 |
WEB OF SCIENCETM
Citations
5
checked on Sep 28, 2024
Page view(s)
120
checked on Sep 7, 2022
Download(s)
224
checked on Sep 7, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.