Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 1306

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

24 votes
Accepted

Does any derivation of commutative algebra preserve its nil-radical?

Suppose $x\in N$, so that $x^n=0$ for some $n$. Then using the product rule for derivations many times, we see that $$ 0=D^n(x^n)=n! D(x)^n+Y, $$ where $Y$ is divisible by $x$. Therefore, $D(x)^{n …
Vladimir Dotsenko's user avatar
17 votes
Accepted

Is the Amitsur-Levitzki identity essentially unique?

The answer to your question is "no", as explained by Anton Klyachko in his answer. Let me refer you to a remarkable statement of Razmyslov and Procesi that describes all identities. They proved (indep …
Vladimir Dotsenko's user avatar
16 votes

What are Homotopy rings good for?

The structure is just that of a graded Lie ring (homologically graded - to create the correct Koszul signs), once you shift degrees by 1. This structure is not at all exotic, you see it in Gerstenhabe …
Vladimir Dotsenko's user avatar
13 votes

Applications of Jordan algebras

I would like to elaborate on the link to "associative" problems (such as the Zelmanov's solution of the restricted Burnside problems mentioned by Tom De Medts) - mainly because by saying that Jordan a …
Vladimir Dotsenko's user avatar
11 votes
Accepted

Koszulness of the cohomology ring of moduli of stable genus zero curves

It is: https://arxiv.org/abs/1902.06318 - this paper also explains how to use the Koszul dual algebra for something, where something is estimating Betti numbers of the free loop spaces of $\overline{M …
Vladimir Dotsenko's user avatar
10 votes
Accepted

Poincaré duality for (co)homology of Lie algebras?

First, let me expand on the reply of Dietrich Burde: I got hold of the paper of Hazewinkel, and can now be more precise about what is and what is not there (last time I saw it was some years ago). …
Vladimir Dotsenko's user avatar
8 votes
0 answers
111 views

Identity for the associator involving a third root of unity

This is a reference request. I came across the class of nonassociative algebras satisfying the following identity: $$ (a,b,c)+\omega(b,c,a)+\omega^2(c,a,b)=0. $$ Here: by an "algebra" I mean a vect …
Vladimir Dotsenko's user avatar
8 votes

How to recognize a Hopf algebra?

A homological condition that might be useful: in the Hopf case, the Yoneda algebra $Ext_A^\bullet(k,k)$ embeds into the Hochschild cohomology $HH^\bullet(A,A)$, moreover, there is a Gerstenhaber algeb …
Vladimir Dotsenko's user avatar
7 votes

Name for algebra and its tensor products

As requested, I elaborate on my comment. First of all, let me make a change of variables $a_i=U_i-1$. The relations then become $a_i+1=a_{i-1}a_{i+1}$. For $n=2,3,4$ I used the Magma online calcula …
Vladimir Dotsenko's user avatar
7 votes
Accepted

Generalizing the Fundamental Theorem of Symmetric Polynomials

I heard of three relatively recent works in that direction, taking different routes and arriving to interesting information about diagonal invariants. First, there is the paper of Vaccarino that Dar …
Vladimir Dotsenko's user avatar
7 votes
Accepted

Subalgebras of quadratic algebras that are not quadratic

Here is an example that shows that you can expect things to get as bad as it goes (I learned about this algebra from the wonderful article The Non-Commutative Gröbner Freaks by Green, Mora, and Ufnaro …
Vladimir Dotsenko's user avatar
7 votes

Linear Algebra Texts?

My personal pick is I.M.Gelfand's "Lectures on linear algebra" (link to a copy on Google Books), accompanied by two warnings: (1) the part "Introduction to tensors" is far from perfect; (2) the proof …
7 votes
Accepted

Curious anti-commutative ring

I noticed this now, and I want to remark that the underlying abelian group can in fact be described very precisely. To do that, note that: (1) the defining relations easily imply that the abelian gro …
Vladimir Dotsenko's user avatar
7 votes
Accepted

Does Manin's construction of non-commutative endomorphism algebra $\mathrm{End}(A)$ produce ...

Q1: This algebra is just the Manin black product of $A$ and $A^!$ (in other words, the Koszul dual of the Segre product of $A$ and $A^!$), and hence it is Koszul. (As requested, the Segre product of t …
Vladimir Dotsenko's user avatar
5 votes

Two (other) rings...are they isomorphic?

This is a bit too long for a comment. Let me denote by $L_k=\sum_i x_i^{k+1}\frac{\partial\phantom{x_i}}{\partial x_i}$ the operators via which vector fields on a line act on polynomials in several …
Vladimir Dotsenko's user avatar

15 30 50 per page