# Tag Info

## Hot answers tagged representation-theory

### Why does group representation theory look linear?

A group in itself is not necessarily related to linear spaces. Representation theory (which is a subfield of group theory) is the study of the way in which groups act linearly on vector spaces : a ...
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### Why does group representation theory look linear?

A group $G$ is an algebraic structure which encodes one pattern of composition of objects. This makes abstract the notion of transformations which may be composed to give new ones. The whole point, ...
• 29.5k
Accepted

### Basic Facts about Lie Algebras

Yes, OP is right: P&S do not distinguish between the abstract Lie group and its defining representation, which is usually the fundamental representation.
• 170k

### Help needed in understanding $2\otimes 2=1\oplus 1\oplus 2$ of $SO(2)$

You can parameterize a general $2\times 2$ matrix of real numbers in terms of 4 real numbers $t$, $a$, $s_1$, and $s_2$ as A = \left( \begin{array} _ \frac{t}{2} + s_1 & s_2 + a \\...
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### Why does group representation theory look linear?

Concerning OP's title question Why does group representation theory look linear? it should be mentioned that there exist in physics (e.g. in the areas of spontaneous symmetry breaking and ...
• 170k
Accepted

### Invariants of inner product in pseudoreal representation of $SU(2)$

P&S are talking about the spinor/defining/fundamental representation $$\eta,\xi~\in~ V~\cong~ \mathbb{C}^2$$ of $SU(2)$. The expression $\epsilon^{\alpha\beta}\eta_{\alpha}\xi_{\beta}$ is $SU(2)$-...
• 170k

### Basic Facts about Lie Algebras

You learnt that in your group theory course, that sounds right. But you must consider the topology. Lie groups are manifolds, so they have tangent spaces (this is an additional structure to being a ...
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• 48.1k
1 vote

### Why does group representation theory look linear?

Linearity is no restriction in the following sense: Every compact Lie group $G$ (in particular every finite group) has a faithful finite-dimensional linear representation, see the Peter-Weyl-theorem. ...
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