Algebra representation

Algebra representation

In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.

ee also

*Module (mathematics)
*Representation theory of Hopf algebras
*Lie algebra representation

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