Skip to main content
MathOverflow

Return to Question

added 131 characters in body
Source Link
Jarek Kędra
Jarek Kędra
  • 1.8k
  • 11
  • 20

It is known that no nontrivial connected cover of $\operatorname{SL}(2,\mathbb R)$ admits a faithful finite dimensional linear representation (see, for example, page 143 in Fulton-Harris and Exercise 11.9 therein). I am looking for a reference with a proof of this fact and an information who observed it first.

EDIT: Textbook reference: Proposition 16.1.7 and Example 16.1.8 in Hilgert and Neeb Structure and Geometry of Lie Groups.

It is known that no nontrivial connected cover of $\operatorname{SL}(2,\mathbb R)$ admits a faithful finite dimensional linear representation (see, for example, page 143 in Fulton-Harris and Exercise 11.9 therein). I am looking for a reference with a proof of this fact and an information who observed it first.

It is known that no nontrivial connected cover of $\operatorname{SL}(2,\mathbb R)$ admits a faithful finite dimensional linear representation (see, for example, page 143 in Fulton-Harris and Exercise 11.9 therein). I am looking for a reference with a proof of this fact and an information who observed it first.

EDIT: Textbook reference: Proposition 16.1.7 and Example 16.1.8 in Hilgert and Neeb Structure and Geometry of Lie Groups.

Source Link
Jarek Kędra
Jarek Kędra
  • 1.8k
  • 11
  • 20

Reference for nonlinearity of covers of $\operatorname{SL}(2,\mathbb R)$

It is known that no nontrivial connected cover of $\operatorname{SL}(2,\mathbb R)$ admits a faithful finite dimensional linear representation (see, for example, page 143 in Fulton-Harris and Exercise 11.9 therein). I am looking for a reference with a proof of this fact and an information who observed it first.