modular representations
Modular representations are a way to study algebraic structures, particularly in the field of representation theory. They focus on how groups, such as finite groups, can be represented through matrices over a field with a specific characteristic, often a prime number. This approach helps mathematicians understand the properties and behaviors of these groups in a more manageable form.
In modular representations, the representations are considered "modular" because they are analyzed over a field that is not large enough to capture all the features of the group. This can lead to interesting phenomena, such as non-semisimple representations, where the usual tools of representation theory do not apply.