Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of Generators for the $2 \times 2$ Matrix Algebra   This paper studies $B(r)$, the space of $r$-tuples of $2 \times 2$ complex
matrices that generate $\operatorname{Mat}_{2 \times 2}(\mathbf C)$ as an
algebra, considered up to change-of-basis. We show that $B(2)$ is homotopy
equivalent to $S^1 \times^{\mathbf Z/2\mathbf Z} S^2$. For $r>2$, we determine
the rational cohomology of $B(r)$ for degrees less than $4r-6$. As an
application, we use the machinery of arXiv:2012.07900 to prove that for all
natural numbers $d$, there exists a ring $R$ of Krull dimension $d$ and a
degree-$2$ Azumaya algebra $A$ over $R$ that cannot be generated by fewer than
$2\lfloor d/4 \rfloor + 2$ elements.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th