Hopf Algebras

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Hopf algebras are abstract algebraic constructions that while confusing to wrap one's head around, have a number of applications in Theoretical Physics e.g. Quantum Mechanics, Dynamical Systems, etc.

There's been a somewhat confusing preprint on arxiv by Adam Nemecek about viewing Transformer Models as Hopf algebras, that seems interesting, but could use some context.

Relevant wiki pages:

• https://en.wikipedia.org/wiki/Tensor_algebra
• https://en.wikipedia.org/wiki/Hopf_algebra

Relevant papers:

• https://arxiv.org/abs/2302.01834
• https://arxiv.org/pdf/math/0408405.pdf

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As a preliminary, we're planning a session on multilinear algebra based on this source to get everyone up to speed on

• Multilinear forms (also dispell the confusion between vectors and covectors)
• Tensors
• Einstein notation After we've done that, we'll already have most of the conceptual tools to tackle Hopf algebras (but it's still 100% worth it on its own)