arXiv subjects

Pete Gautam

Publications and source records attributed to Pete Gautam.

3 recordsLinked to original sources

arXiv2026

Fusion Systems on Sylow $3$-subgroups of Fischer and Monster sporadic groups -- II

We classify all corefree fusion systems on a Sylow 3-subgroup of the sporadic groups $\mathrm{Fi}_{24}'$ and $\mathrm{M}$. The program to classify of all corefree fusion systems on Sylow $p$-subgroups of sporadic groups has been running for many years, comprising of work done in several papers by numerous authors. We complete this program for $p$ odd. In the process, we expand the theory of proto-essential subgroups and describe algorithms that make the process of finding all corefree fusion systems on a $p$-group better by several orders of magnitude.

math.GR↗

arXiv2026

Fusion Systems on Sylow $3$-subgroups of Fischer and Monster sporadic groups: I

We classify all corefree fusion systems on a Sylow $3$-subgroup of the sporadic groups $\mathrm{Fi}_{22}$, $\mathrm{Fi}_{23}$ and $\mathrm{B}$. We show that the $3$-group in each case does not support any exotic fusion systems. This is the first of two papers that will complete the classification of all corefree fusion systems on Sylow $p$-subgroups of sporadic groups for $p$ odd.

math.GR↗

arXiv2022

On strong shift equivalence for row-finite graphs and C*-algebras

This note extends and strengthens a theorem of Bates that says that row-finite graphs that are strong shift equivalent have Morita equivalent graph C*-algebras. This allows us to ask whether our stronger notion of Morita equivalence does in fact characterise strong shift equivalence. We believe this will be relevant for future research on infinite graphs and their C*-algebras. We also study insplits and outsplits as particular examples of strong shift equivalences and show that the induced Morita equivalences respect a whole family of weighted gauge actions. We then ask whether strong shift equivalence is generated by (generalised) insplits and outsplits.

math.OA↗