Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Good day all. I am wondering about a possible classification result.

Consider the Grassman algebra $\bigwedge V$ for a vector space $V$ of finite dimension. Is there a simple characterization of the simple modules over $\bigwedge V$? As in, how can we describe them all up to isomorphism? I did not see this result in my books, so I thought I ask here. Thank you.

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

As noted here: Are projective modules over exterior algebras of vector spaces necessarily free? the exterior algebra is local, and hence has only one maximal right ideal, call it M. Any simple module must therefore be isomorphic to the right $R$ module $\bigwedge(V)/M$.

Similarly, the simple left modules are isomorphic to the left $R$ module $\bigwedge(V)/M$.

share|improve this answer
    
Thanks you for this. –  Camilla Vaernes Apr 28 '12 at 2:03
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.