And they didn’t stop there.
Representation theory transforms abstract algebra groups into things like simpler matrices.The field’s founder left a list of 43 problems for others to study, iterate on, and prove.One mathematician has helped to prove both one of these and another problem just this year.Mathematician Pham Huu Tiep and his colleagues have made a proof of one longstanding open problem and one additional foundational question in a subfield of abstract algebra known as representation theory.
Each element has a ‘height’ that describes whether or not it can be divided cleanly by another element. If so, the result of that division is the height.Brauer laid out a list of problems that help to define representation theory. Number 23 is the Height Zero Conjecture, in which Brauer claims that abelian groups must have a particular quality related to the heights of their elements.
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