Large Algebra Collider (LAC) | Thom polynomial portal

Large Algebra Collider (LAC) — Elementary splittings of certain algebras.

These splittings determine the hierarchy of multi-singularities.

$\mu=1$

A1 -> 2*A0

$\mu=2$

A2 -> A0+A1

III22 -> A2

$\mu=3$

A3 -> 2*A1, A0+A2

I22 -> III22, A3

III23 -> I22, A0+III22

C3 -> III23

$\mu=4$

A4 -> A1+A2, A0+A3

I23 -> III23, A4, A0+I22

III24 -> I23, A1+III22, A0+III23

III33 -> I23, A0+III23

B4 -> III33, III24

C41 -> I23 (l=2) — C41 -> I23, C3 (l=3)

C42 -> C41, B4

C43 -> C42, A0+C3

D4 -> ?

$\mu=5$

A5 -> 2*A2, A1+A3, A0+A4

I24 -> III24, A5, A1+I22, A0+I23

I33 -> III33, A5, A0+I23

III25 -> I24, A2+III22, A1+III23, A0+III24

III34 -> I33, I24, A1+III23, A0+III33, A0+III24

B51 -> B4, I33, I24

B52 -> B51, III34, III25, A0+B4

B53 -> B52, 2*III22

B54 -> B52

C51 -> B4, I24, A0+III33 (l=1) — C51 -> C42, I24, A0+III33 (l=2)

C52 -> C51, B51, III34, A0+B4

C53 -> C42, B51, A0+C41

C54 -> C52, B52

C55 -> C53, C52, A0+C42

C56 -> C53, B52, A0+C42

C57 -> C56, C55, C54

$\mu=6$

A6 -> A2+A3, A1+A4, A0+A5

I25 -> III25, A6, A2+I22, A1+I23, A0+I24

I34 -> III34, A6, A1+I23, A0+I33, A0+I24

III26 -> I25, A3+III22, A2+III23, A1+III24, A0+III25

III35 -> I34, I25, A2+III23, A1+III33, A0+III34, A0+III25

III44 -> I34, A1+III24, A0+III34

B6 -> B52, I34, I25, A0+B51

C6 -> C52, B52, I34, I25, A1+III33, A0+C51, A0+III34 (l=1) — C6 -> C56, C55, I34, I25, A1+III33, A0+C51, A0+III34 (l=2)