Abstract
We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from $$\mathbf {PSL}_n(q)$$
PSL
n
(
q
)
collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is $$\mathbf {PSp}_{2n}(q)$$
PSp
2
n
(
q
)
, $$\mathbf {P}{\varvec{\Omega }}^+_{4n}(q)$$
P
Ω
4
n
+
(
q
)
, $$\mathbf {P}{\varvec{\Omega }}^-_{4n}(q)$$
P
Ω
4
n
-
(
q
)
, $$^3D_4(q)$$
3
D
4
(
q
)
, $$E_7(q)$$
E
7
(
q
)
, $$E_8(q)$$
E
8
(
q
)
, $$F_4(q)$$
F
4
(
q
)
, or $$G_2(q)$$
G
2
(
q
)
with q even is the group algebra.
Pointed Hopf algebras over the sporadic simple groups