Projective special linear group of degree two: Difference between revisions

Revision as of 23:54, 27 October 2010

Definition

The projective special linear group of degree two over a field $k$ , or more generally over a commutative unital ring $R$ , is defined as the quotient of the special linear group of degree two over the same field or commutative unital ring by the subgroup of scalar matrices in that group. The group is denoted by $P S L (2, R)$ or $P S L_{2} (R)$ .

Elements

Further information: element structure of projective special linear group of degree two

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 ==Definition==
-==Definition==
+The '''projective special linear group of degree two''' over a [[field]] <math>k</math>, or more generally over a [[commutative unital ring]] <math>R</math>, is defined as the quotient of the [[defining ingredient::special linear group of degree two]] over the same field or commutative unital ring by the subgroup of scalar matrices in that group. The group is denoted by <math>PSL(2,R)</math> or <math>PSL_2(R)</math>.
-The '''special linear group of degree two''' over a [[field]] <math>k</math>, or more generally over a [[commutative unital ring]] <math>R</math>, is defined as the quotient of the [[defining ingredient::special linear group of degree two]] over the same field or commutative unital ring by the subgroup of scalar matrices in that group. The group is denoted by <math>PSL(2,R)</math> or <math>PSL_2(R)</math>.
+==Elements==
+{{further|[[element structure of projective special linear group of degree two]]}}