All Questions
Tagged with noncommutative-algebra reference-request
57 questions
43
votes
8
answers
3k
views
How to quantify noncommutativity?
If I have two operators or finite-dimensional matrices $A$ and $B$, how can I quantify the amount to which they commute or don't commute? (I would consider it a big plus if it is computable easily for ...
- 1,890
21
votes
4
answers
7k
views
Binomial Expansion for non-commutative setting
What could be a reference about binomial expansions for non-commutative elements?
Specifically, where can I find a closed formula for the expansion of $(A+B)^n$ where $[A,B]=C$ and $[C,A]=[C,B]=0$?
...
- 829
4
votes
3
answers
567
views
Gröbner/SAGBI bases for non-commutative setting
It is well known that SAGBI/Gröbner bases are important for commutative and non-commutative algebra. The references for commutative scenery is ample and vast, but I am in trouble to find a good ...
- 829
6
votes
0
answers
998
views
Generalized Courant-Fischer theorem
Consider some quaternionic matrix $A$. A right eigvenvalue of $A$ is a quaternion $q$ such that $Ax=xq$ for some $x\in \mathbb{H}^n$. Similarly, a left eigenvalue of $A$ is quaternion $q$ such that $...
- 475
4
votes
3
answers
1k
views
Set of invertible operators in B(H) is connected. Is it true? Is there a reference?
Suppose $H$ is a Hilbert space, $B(H)$ is the algebra of bounded linear operators on it, $K(H)$ is ideal of compact operators in $B(H)$, $Inv(B(H)/K(H))$ is the topological group of invertible ...
- 1,284
5
votes
1
answer
2k
views
Length of a module over different rings
Given a regular local ring $(R,m)$ and a finitely generated $R$-algebra $S$, which is free as an $R$-module. Let $M$ be a left $S$-module of finite length, $\ell_S(M)=r<\infty$.
Under what ...
- 1,391
4
votes
1
answer
334
views
Non-commutative versions of X/G
Let $X$ be a Riemannian manifold and let $G$ be a (at most countable, if that matters) discrete group acting properly and by isometries on $X$. Let $\mathcal{O}$ be the sheaf of analytic functions on ...