# Fortnightly links (19)

Shame on me for not posting this yesterday, but I can blame the jet lag of coming back from Banff together with the last minute things for the organisation of Antwerp.

An atlas of subgroup lattices of finite almost simple groups is some fun data on the subgroup lattices of various interesting finite groups.

Kulkarni, Lieblich: Blt Azumaya algebras and moduli of maximal orders is an interesting update to an earlier preprint. It describes (compactifications of) moduli of maximal orders as

*two different*moduli stacks*with the same closed points*. One description is as a substack of the moduli stack of coherent algebras on the original scheme. The other description uses a nifty root stack construction to create a stack on which one can consider Azumaya algebras. Cool!The main reason why Max Lieblich wanted to write this was to use the abbrevation blt. He succeeded.

Sue Sierra, A family of quantized projective spaces is one of the many exciting talks from last week's conference. What she did is turn the new and somewhat weird construction in section 3.6 of Pym's deformations of $\mathbb{P}^3$ into a whole family of twisted Calabi–Yau algebras, depending on an integer $n$ and a scalar $a$. She moreover explains why a certain value for $a$ is needed in Pym's setting (he works untwisted Calabi–Yau) if $n=4$, but her families exist for every value of $n$. And for $n=3$ (i.e. For a noncommutative $\mathbb{P}^2$) her construction has as underlying elliptic curve the conic and a tangent line.

If I remember correctly she also describes the point scheme for higher values of $n$. I'll leave that as an fun exercise to find out.