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8 votes
2 answers
2k views

Reason to apply the Koszul sign rule everywhere in graded contexts

The Koszul sign rule is a sign rule that arises from graded-commutative algebras. For instance, let $\bigwedge(x_1,\dots, x_n)$ be the free graded-commutative algebra generated by $n$ elements of ...
Javi's user avatar
  • 499
3 votes
2 answers
255 views

Is being graded commutative a necessary condition on $A$ such that $H^*(A)$ is commutative?

If we consider any differential graded algebra $A^\bullet$, then its homology is a graded algebra, since the tensor product interacts well with homology. A sufficient condidtion for the homology to be ...
curious math guy's user avatar
1 vote
0 answers
85 views

Exponential of a sum in a non-commutative graded algebra

Let $a,b$ be two elements of a graded algebra $A$ such that $\deg(a)=1$, $\deg(b)=0$ and $[a,b]\neq 0$. I would like to know whether there exits an explicit expression for the degree 1 component $$\...
BinAcker's user avatar
  • 789
1 vote
0 answers
60 views

Universal bimodule for homotopy biderivations

Recall the commutative story: for a commutative algebra $A$, its module of differentials $\Omega (A)$ is characterized by the universal property that any derivation $\delta \colon A \to M$ is in a ...
Dasha Poliakova's user avatar