Burnside rings for Real 2-representation theory: The linear theory
نویسندگان
چکیده
منابع مشابه
Certain Applications of the Burnside Rings and Ghost Rings in the Representation Theory of Finite Groups (ii)
Using the Burnside ring theoretic methods a new setting and a complete description of the Artin exponent A(G) of finite p-groups was obtained in [4]. In this paper, we compute A(G) for any finite group G – hence providing the global version of [4].
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We study 2-representations, i.e. actions of 2-groups on 2-vector spaces. Our main focus is character theory for 2-representations. To this end we employ the technique of extended Burnside rings. Our main theorem is that the Ganter-Kapranov 2-character is a particular mark homomorphism of the Burnside ring. As an application we give a new proof of Osorno formula for the Ganter-Kapranov 2-charact...
متن کاملBurnside rings
1 Let G be a finite group. The Burnside ring B(G) of the group G is one of the fundamental representation rings of G, namely the ring of permutation representations. It is in many ways the universal object to consider when looking at the category of G-sets. It can be viewed as an analogue of the ring Z of integers for this category. It can be studied from different points of view. First B(G) is...
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Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby’s problem list, this question is called The Montesinos-Nakanishi 3-move conjecture. We define the nth Burnside group of a link and use the 3rd Burnside group to answer Nakanishi’s question. One of the oldest elementary formulated problems in classical Knot Theory is the 3move conjecture of Nakanishi. A 3-move...
متن کاملThe Burnside Groups and Small Cancellation Theory
In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the fi...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2020
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199720500121