[redacted]

Advertisements

Skip to content
#
representation theory

# Deranged cohomology

# An indecomposable module

# A generalization of Schur’s lemma

# Some representation theory

[redacted]

Advertisements

Suppose and let be a proper ideal containing all monomials of degree . Then is an indecomposable -module.

(Dixmier) Let be a -algebra (in fact, any uncountable algebraically closed field will do) and be a simple -module having a countable basis as a -vector space. Then .

Brief outline:

- By Schur’s lemma, is a division algebra. Moreover, it has a countable basis.
- Suppose does not act as a scalar. Then is trascendental over .
- This is absurd since it would imply has uncountable dimension.

Find all representations over of the group of matrices

where and are in .