Associated linear representation

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What does "The associated linear representation of a group or a semigroup" or "The representation associated to a module" mean?

edited Jun 29 at 16:53

asked Jun 29 at 16:33

Jamal
11●2

Associated to what? What is the context? – Qiaochu Yuan Jun 29 at 16:50

If A is an algebra over a field K, and V is an A-module. Does the associated linear representation of V mean the regular representation f from A into End_K(V), with f(a)(v)=a.v, for each a in A and v in V? – Jamal Jun 29 at 17:32

Where is the group or semigroup? – Qiaochu Yuan Jun 29 at 17:50

The algebra A can be replaced with a group or a semigroup. – Jamal Jun 29 at 18:06

Yes, it means what you wrote in your first comment. Except that probably you don't want to call that the "regular" representation. The regular representation usually means the representation of an algebra on itself by (left) multiplication. Voting to close, as this is not a research-level question. – MTS Jun 29 at 19:52