Wikipedia:Reference desk/Archives/Mathematics/2013 February 24

= February 24 =

Terminology in Representation Theory
Suppose one has an action of a group G on a vector V space and a map $$ that is not a homomophism into GL(V) but instead satisfies $Π(g_{1}g_{2}) = Π(g_{2})Π(g_{1})$. Is there a standard name for such an "anti-representation"? Same question for Lie algebras; $π([X,Y]) = - [π(X),π(Y)]$? YohanN7 (talk) 20:43, 24 February 2013 (UTC)


 * What you are describing is a right group action on the vector space. (Usually groups are thought of as acting on the left.)  The same with the Lie algebra.   Sławomir Biały  (talk) 21:15, 24 February 2013 (UTC)


 * Aha, thank you sir! That was too obvious for me to think of. YohanN7 (talk) 23:23, 24 February 2013 (UTC)