# Questions tagged [symmetric-algebras]

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8
questions

**6**

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**1**answer

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### Is the (super-)symmetric power of the exterior algebra free?

Let $V$ be a vector space over $k$ of dimension $m$. (I'm only interested in the case $k=\mathbb{Q}$.) Let $R:=\Lambda^*V$ be the exterior algebra. It carries the structure of a supercommutative ring: ...

**6**

votes

**1**answer

148 views

### Symmetric algebras of given dimension

Fix an algebraically closed field $F$. Are there only finitely many symmetric algebras with unit over $F$ of a given finite dimension (up to isomorphism)? By symmetric I mean a Frobenius algebra where ...

**3**

votes

**0**answers

306 views

### 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\...

**5**

votes

**1**answer

350 views

### A nice generating set for the symmetric power of an algebra

I'm looking for a reference for the following fact.
Suppose $A$ is a finitely generated associative commutative unital algebra over an algebraically closed field of characteristic zero. Let $S^n(A)$ ...

**6**

votes

**1**answer

857 views

### Coderivations of S(V) correspond to linear maps S(V) -> V. Only over characteristic 0?

Definition. Let $k$ be a commutative ring. Let $V$ be a $k$-module. We turn the symmetric algebra $\mathrm{S}\left(V\right)$ of $V$ into a graded Hopf algebra by defining the comultiplication
$\Delta ...

**1**

vote

**1**answer

529 views

### Restricted universal enveloping algebra of Abelian p-Lie algebra

Question: Let $p$ be a prime. Let $k$ be a commutative ring such that $p=0$ in $k$.
Let $\mathfrak g$ be an abelian $p$-restricted Lie algebra over $k$. In other words, let $\mathfrak g$ be a $k$-...

**13**

votes

**2**answers

815 views

### Where is there a treatment of “exponential monads”?

I have a category $C$, which is equipped with a symmetric monoidal structure (tensor product $\otimes$, unit object $1$). My category also has finite coproducts (I'll write them using $\oplus$, and ...

**1**

vote

**1**answer

608 views

### Are cyclotomic Khovanov-Lauda-Rouquier algebras symmetric?

Recall that for k a field, a finite dimensional k-algebra A is called symmetric if it is isomorphic to its dual as a bimodule of itself. Which is to say, there's a trace map t:A -> k such that t(ab)=...