In the first version of Problem 2(a), I had written . The current formulation says . These statements are equivalent (can you see why?), but I want you to prove the current formulation.

Problem 2(c) should say:

Prove that as -algebras.

Problem 3 should say: “A nonzero element is grouplike if and only if .”

In Problem 5(c), the algebra is called $\wedge(V)$.

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Really Basic Undergrad Question, and I’ve been putting off puttering with it because there’s other stuff to be done: If is injective, and , then obviously . However, can we conclude that both and are invertible?

(This, btw, is related to something I was doing with the Universal Property and mappings)

In the first version of problem 2.a. we can state that because as -algebras, right?