MSC: Primary 20C20; Secondary 16D90, 20C05
DOI: 10.21538/0134-4889-2021-27-1-220-239
Full text
This paper is based on the results of the 2020 Ural Workshop on Group Theory and Combinatorics.
We classify the Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two.
Keywords: Donovan’s conjecture, finite groups, Morita equivalence, block theory, modular representation theory
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Received September 6, 2020
Revised October 1, 2020
Accepted October 5, 2020
Funding Agency: This paper is part of the work done by the author during his PhD at the University of Manchester, supported by a Manchester Research Scholar Award and a President’s Doctoral Scholar Award.
Cesare Giulio Ardito, Department of Mathematics, City University of London, Northampton Square, London, EC1V 0HB, United Kingdom, email: cesareg.ardito@gmail.com
Cite this article as: Cesare Giulio Ardito, Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 1, pp. 220–239.
Русский
Ч.Дж. Ардито. Классы Морита-эквивалентности главных блоков с элементарными абелевыми дефектными группами порядка 64
Дана классификация классов Морита-эквивалентности главных блоков с элементарными абелевыми дефектными группами порядка 64 относительно полного кольца дискретного нормирования с алгебраически замкнутым полем вычетов характеристики 2.
Ключевые слова: гипотеза Донована, конечные группы, Морита-эквивалентность, теория блоков, теория модулярных представлений
