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When I first saw a definition of a supercommutative algebra, first example that came to my mind was an exterior algebra on some vector space. Of course, purely even supercommutative algebra is just a commutative algebra, so we count commutative algebras as examples of supercommutative algebras.

I'm left wondering: what are some other examples of supercommutative algebras? Of course, you can use a cheap trick and consider a direct sum of a (nontrivial) commutative and (nontrivial) exterior algebra, and get an algebra that is neither commutative or exterior.

So, maybe a better posed question is: are there supercommutative algebras which do not come from ''combinations'' of commutative and exterior algebras?

ante.ceperic
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At least over a field $k$ of characteristic $\neq 2$, the answer to your question is "no", it will always be a quotient of a commutative algebra tensored with an exterior algebra.

More concretely, let $\theta_i$ be a choice of odd indeterminates, then any supercommutative algebra $A$ over $k$ is a quotient of $k[x_1, \cdots, x_m] \otimes_k \bigwedge_k(\theta_1, \cdots , \theta_n)$ by some homogeneous ideal $Q$ and some $m,n \in \mathbb{N}$. Here an ideal $Q$ of a supercommutative algebra over $k$ is called homogeneous iff $Q=(Q \cap A_0) \oplus (Q \cap A_1)$.

user7090
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