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Results tagged with higher-algebra
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user 124549
1
vote
1
answer
147
views
Classification of finite crossed modules
A finite crossed module is a 4-tuple
$$(G_1,G_2,\delta: G_2 \to G_1, \alpha: G_1 \to Aut(G_2))$$
satisfying certain compatible conditions, where the $G_i$ are finite groups and the maps are group homo …
- 5,230
4
votes
0
answers
186
views
Cohomology and higher structures
Classically, cohomologies of Lie groups/algebras parametrize extensions. To be precise, given an linear $G$-action on $M$, there is an bijection between $H^2(G;M)$ and the set of extension $E$ of $G$ …
- 5,230
7
votes
0
answers
220
views
Representations of 2-groups and quantum double constructions
Let $G$ be a finite group. The category of its representations (complex linear, finite dimensional, throughout this whole question) is equivalent to $\mathbb{C}[G]$-modules. V. Drinfeld constructed a …
- 5,230