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

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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(g₁g₂) = Π(g₂)Π(g₁). 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)