Search Results

This is in P. M. Cohn, "On the Embedding of Rings in Skew Fields", Proceedings of the London Mathematical Society, Volume s3-11, Issue 1 (1961), Pages 511-530. I do not think that the zero characteris …

Yes, it is true. In fact, it is true that $H^i(K_{2n+1},F)=0$ for $0<i\le 2n$. This can be deduced from the theorem of Feigin sketched in Feigin, B.L. Cohomology of contact Lie algebras. (Russian) C. …

A quick Google search shows that most of Nieuw Arch. Wisk. is digitized; you can find the relevant volume here.

There are lots of papers dealing with representation-theoretic questions and universal enveloping algebras using Gröbner bases. Some examples are given by these: 1, 2, 3, 4.

This is a difficult and very interesting question. As explained in comments and the other answer, the problem is as stated is "wild", but There are many special versions of it where something can be s …

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 …

This seems to first have been considered by Dirac under the name "quantum Poisson bracket" - an easy accessible reference is Fock's "Fundamentals of Quantum Mechanics", discussion around formula (2.10 …

I recall seeing in various sources the terminology "cover preserving embedding" and "cover preserving subposet". Googling it now (https://www.google.com/search?q=poset+%22cover+preserving%22) brings s …

Another possibility is to consider group elements rather than commutators. If you take the matrices $A=\mathrm{diag}(1,\xi,\ldots,\xi^{n-1})$ and $B=\begin{pmatrix}0&1&0&\cdots&0&0\\ 0&0&1&\cdots&0&0\ …

According to https://zbmath.org/?q=an:0242.60018 , it was translated in Soviet Mathematics. Doklady (https://zbmath.org/serials/?q=se%3A00000717), but I doubt it was digitised, so you just need to dem …

I think that there is just a little mess between things that are denoted $K$, $K'$ in the book, as well as $d$, $d'$. For that, let us examine these formulas carefully. Using the first formula for the …

Multilinear equations are hardly easier than general equations. For instance, the multilinear equations $$ \begin{cases} x_0-x_1=0,\\ x_0x_1-x_2=0,\\ x_0x_2-x_3=0,\\ \ldots\\ x_0x_{n-1}-x_n=0 \end{c …

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 …

There are two very famous instances of Jack polynomials in relationship to the Virasoro algebra (there are some others, but they very often seem to be related to one of these): Katsuhisa Mimachi and …

For $k=\infty$, this algebra appears when studying integrable representations of level 1 of the Lie algebra $\widehat{\mathfrak{sl}}_2$, see, for example, discussion in Section 2 of A. V. Stoyanovs …