An exact sequence for the graded Picent
-
Andrei Marcus
and
Virgilius-Aurelian Minuță
Abstract
To a strongly 𝐺-graded algebra 𝐴 with 1-component 𝐵, we associate the group
Funding source: Ministerul Cercetării, Inovării şi Digitalizării
Award Identifier / Grant number: PN-III-P4-ID-PCE-2020-0454
Funding statement: This research is supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI–UEFISCDI, project number PN-III-P4-ID-PCE-2020-0454, within PNCDI III.
-
Communicated by: Olivier Dudas
References
[1] M. Beattie and A. del Río, The Picard group of a category of graded modules, Comm. Algebra 24 (1996), no. 14, 4397–4414. 10.1080/00927879608825823Search in Google Scholar
[2] R. Boltje, R. Kessar and M. Linckelmann, On Picard groups of blocks of finite groups, J. Algebra 558 (2020), 70–101. 10.1016/j.jalgebra.2019.02.045Search in Google Scholar
[3] E. C. Dade, Block extensions, Illinois J. Math. 17 (1973), 198–272. 10.1215/ijm/1256051756Search in Google Scholar
[4] E. C. Dade, Extending irreducible modules, J. Algebra 72 (1981), no. 2, 374–403. 10.1016/0021-8693(81)90300-8Search in Google Scholar
[5] C. W. Eaton and M. Livesey, Some examples of Picard groups of blocks, J. Algebra 558 (2020), 350–370. 10.1016/j.jalgebra.2019.08.004Search in Google Scholar
[6] A. Marcus, On Picard groups and graded rings, Comm. Algebra 26 (1998), no. 7, 2211–2219. 10.1080/00927879808826271Search in Google Scholar
[7] A. Marcus, Representation Theory of Group Graded Algebras, Nova Science, Commack, 1999. Search in Google Scholar
[8] A. Marcus and V.-A. Minuță, Group graded endomorphism algebras and Morita equivalences, Mathematica 62(85) (2020), no. 1, 73–80. 10.24193/mathcluj.2020.1.08Search in Google Scholar
[9] A. Marcus and V.-A. Minuță, Character triples and equivalences over a group graded 𝐺-algebra, J. Algebra 565 (2021), 98–127. 10.1016/j.jalgebra.2020.07.029Search in Google Scholar
[10] J. Neukirch, A. Schmidt and K. Wingberg, Cohomology of Number Fields, 2nd ed., Grundlehren Math. Wiss. 323, Springer, Berlin, 2008. 10.1007/978-3-540-37889-1Search in Google Scholar
[11] I. Reiner Maximal Orders, London Math. Soc. Monogr. (N. S.) 28, Clarendon Press, Oxford, 2003. 10.1093/oso/9780198526735.001.0001Search in Google Scholar
[12] B. Späth, Reduction theorems for some global-local conjectures, Local Representation Theory and Simple Groups, EMS Ser. Lect. Math., European Mathematical Society, Zürich (2018), 23–61. 10.4171/185-1/2Search in Google Scholar
[13] C. A. Weibel, An Introduction to Homological Algebra, Cambridge Stud. Adv. Math. 38, Cambridge University, Cambridge, 1994. 10.1017/CBO9781139644136Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Virtual planar braid groups and permutations
- Orders on free metabelian groups
- The Reidemeister spectrum of direct products of nilpotent groups
- Structure of the Macdonald groups in one parameter
- Finite groups with modular 𝜎-subnormal subgroups
- Invariance of the Schur multiplier, the Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
- An exact sequence for the graded Picent
Articles in the same Issue
- Frontmatter
- Virtual planar braid groups and permutations
- Orders on free metabelian groups
- The Reidemeister spectrum of direct products of nilpotent groups
- Structure of the Macdonald groups in one parameter
- Finite groups with modular 𝜎-subnormal subgroups
- Invariance of the Schur multiplier, the Bogomolov multiplier and the minimal number of generators under a variant of isoclinism
- An exact sequence for the graded Picent
