Questions tagged [symmetric-algebras]

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Symmetric power of an algebra

Given an algebra $A$ over $k$ with characteristic zero and a positive integer $n$, the subspace of $A^{\otimes n}$ consisting of all tensors invariant under the action of all permutations $\sigma\in\...
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Almost split sequences for symmetric algebras

Let $k$ be an algebraically closed field and $A$ be a symmetric algebra. I want to know how to compute almost split sequences ending at a non-projective indecomposable right $A$-module $X$. Question: ...
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Symmetric algebra of monomial ideal modulo a binomial ideal isomorphic to a quotient of a polynomial ring

Note: I posted this question on MSE but haven't received any response. I’m trying to understand the proof of Corollary 1.9 in “Binomial ideals” by David Eisenbud and Bernd Sturmfels. Notation: Let $S= ...
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What comes next in the sequence "symmetric algebras, exterior algebras, divided power algebras, ..."?

This question was posed by A Rock and a Hard Place in this discussion, where they mentioned the isomorphisms \begin{align*} \mathrm{L}\,\mathrm{Sym}^n_R(M[1]) &\cong (\mathrm{L}\,{\...
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What is the definition of this function?

I'm reading a paper and I didn't understand this notation used by the author: Let E be a vector space and F be a subspace of E. Let $S(E/F)$ be the symmetric algebra of $E/F$. For every element $P \...
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