TY - JOUR
T1 - RELATIVE CELLULAR ALGEBRAS
AU - Ehrig, M.
AU - Tubbenhauer, D.
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/3
Y1 - 2021/3
N2 - In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are relative cellular, but not cellular: most prominently, the restricted enveloping algebra and the small quantum group for sl2, and an annular version of arc algebras.
AB - In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are relative cellular, but not cellular: most prominently, the restricted enveloping algebra and the small quantum group for sl2, and an annular version of arc algebras.
UR - http://www.scopus.com/inward/record.url?scp=85075231947&partnerID=8YFLogxK
U2 - 10.1007/s00031-019-09544-5
DO - 10.1007/s00031-019-09544-5
M3 - Article
AN - SCOPUS:85075231947
SN - 1083-4362
VL - 26
SP - 229
EP - 277
JO - Transformation Groups
JF - Transformation Groups
IS - 1
ER -