Questions tagged [symmetric-algebras]
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questions with no upvoted or accepted answers
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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 \...