nLab
2representation
Contents
Context
Representation theory
representation theory
geometric representation theory
Ingredients
Definitions
representation, 2representation, ∞representation

group, ∞group

group algebra, algebraic group, Lie algebra

vector space, nvector space

affine space, symplectic vector space

action, ∞action

module, equivariant object

bimodule, Morita equivalence

induced representation, Frobenius reciprocity

Hilbert space, Banach space, Fourier transform, functional analysis

orbit, coadjoint orbit, Killing form

unitary representation

geometric quantization, coherent state

socle, quiver

module algebra, comodule algebra, Hopf action, measuring
Geometric representation theory

Dmodule, perverse sheaf,

Grothendieck group, lambdaring, symmetric function, formal group

principal bundle, torsor, vector bundle, Atiyah Lie algebroid

geometric function theory, groupoidification

EilenbergMoore category, algebra over an operad, actegory, crossed module

reconstruction theorems
Theorems
Contents
Idea
A 2representation of a 2group $G$ is an infinityaction of $G$ on a 2vector space $V$. The higher analog of the representation of a group.
References
 Zhen Huan, 2Representations of Lie 2groups and 2Vector Bundles (arXiv:2208.10042)
Last revised on August 23, 2022 at 14:26:32.
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