4d-AS-regular

the classification of 4-dimensional Artin–Schelter regular algebras

A website dedicated to the classification and properties of four-dimensional Artin–Schelter regular algebras, organised around the known families and the data of arXiv:2511.08390 .

See explained for the definitions and families for the full presentations. Click a column heading to sort.

familydefinedparametersdimension point scheme\(\mathrm{HH}^i_0\)\(\mathrm{HH}^i(\mathrm{qgr}\,A)\)
123123
Sklyanin198221129027
skew199061464335
Vancliff199432343247
Vancliff twist199431343247
Clifford1995240191901520
central extension of Sklyanin199612117190712
Shelton–Tingey20010?117———
double Ore A2009112221812
double Ore B20091121011721
double Ore C200911210104
double Ore D2009212221812
double Ore E200911210236
double Ore F20091121011620
double Ore G2009312221812
double Ore H200921331368
double Ore I20091121011620
double Ore J200911210236
double Ore K200931331214
double Ore L200931331368
double Ore M2009212223911
double Ore N20093122211519
double Ore O2009212223911
double Ore P20092122211519
double Ore Q200911210115
double Ore R200912210269
double Ore S20091121011721
double Ore T2009112102811
double Ore U2009112102811
double Ore V200911210115
double Ore W20092122211519
double Ore X200911331368
double Ore Y20092123411620
double Ore Z20092122211519
Cassidy–Vancliff 120101011701621
Cassidy–Vancliff 2201040191901621
Cassidy–Vancliff 3201040197———
L(1,1,2) σ201551248137
Pym S(2,3)201561499368
R(3,a)201611211104
\(S_\infty\)201621125027
\(S_\infty\) twist201620181701419
Sklyanin twist201620182101419
deformed skew \((x_3x_2;\ x_4^2)\)?5?343———
deformed skew \((x_2x_1;\ x_3x_4)\)?5?343———
deformed skew \((x_3x_2;\ x_4^2, x_1^2)\)?5?248———
deformed skew \((x_3x_1, x_3x_2;\ x_4^2)\)?4?222———
deformed skew \((x_2x_1, x_3x_2;\ x_3^2, x_4^2)\)?4?222———