#representationtheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #representationtheory, aggregated by home.social.
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Quiver algebras have the property that, in any fixed dim, rep(Q) is a vector space. Is there some characterization of which algebras have this property?
(Unital algebras seem to be ruled out. Except kQ *is* unital, but for those you can just "throw away" the 1, and all the primitive idempotents in fact, and it works. I guess it's because they have an k-linear decomposition \(kQ = E \oplus I\) where E is the subalgebra of idempotents and I is an ideal, and any representation of Q is uniquely determined by what it does on I (which is a non-unital subalgebra), since it has no choice of what to do on E. Not quite sure what the right general principle is here though...)
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Anyone know the tame/wild classification for finite *cyclic* quivers? The oft-quoted one is for acyclic.
I can see any quiver w/ two cycles is wild, and any graph that is just one cycle is tame. Having trouble finding anything written about classifying other unicyclic quivers.
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Quantum mechanics anyone? Dozens have been disappointed by UCLA’s administration ineptly standing in the way of Dr. Mike Miller being able to offer his perennial Winter UCLA math class (Ring Theory this quarter), so a few friends and I are putting our informal math and physics group back together.
We’re mounting a study group on quantum mechanics based on Peter Woit‘s Introduction to Quantum Mechanics course from 2022. We’ll be using his textbook Quantum Theory, Groups and Representations:An Introduction (free, downloadable .pdf) and his lectures from YouTube.
Shortly, we’ll arrange a schedule and some zoom video calls to discuss the material. If you’d like to join us, send me your email or leave a comment so we can arrange meetings (likely via Zoom or similar video conferencing).
Our goal is to be informal, have some fun, but learn something along the way. The suggested mathematical background is some multi-variable calculus and linear algebra. Many of us already have some background in Lie groups, algebras, and representation theory and can hopefully provide some help for those who are interested in expanding their math and physics backgrounds.
Everyone is welcome!
#group-theory #lie-groups #peter-woit #physics #quantum-mechanics #representation-theory
https://boffosocko.com/2023/01/26/quantum-mechanics-study-group-for-peter-woit/