TY - JOUR
T1 - Exponentiation of commuting nilpotent varieties
AU - Sobaje, Paul
N1 - Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - Let H be a linear algebraic group over an algebraically closed field of characteristic p > 0. We prove that any "exponential map" for H induces a bijection between the variety of r-tuples of commuting [. p]-nilpotent elements in Lie(H) and the variety of height r infinitesimal one-parameter subgroups of H. In particular, we show that for a connected reductive group G in pretty good characteristic, there is a canonical exponential map for G and hence a canonical bijection between the aforementioned varieties, answering in this case questions raised both implicitly and explicitly by Suslin, Friedlander, and Bendel.
AB - Let H be a linear algebraic group over an algebraically closed field of characteristic p > 0. We prove that any "exponential map" for H induces a bijection between the variety of r-tuples of commuting [. p]-nilpotent elements in Lie(H) and the variety of height r infinitesimal one-parameter subgroups of H. In particular, we show that for a connected reductive group G in pretty good characteristic, there is a canonical exponential map for G and hence a canonical bijection between the aforementioned varieties, answering in this case questions raised both implicitly and explicitly by Suslin, Friedlander, and Bendel.
UR - http://www.scopus.com/inward/record.url?scp=85028162353&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2014.07.031
DO - 10.1016/j.jpaa.2014.07.031
M3 - Article
AN - SCOPUS:85028162353
SN - 0022-4049
VL - 219
SP - 2206
EP - 2217
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 6
ER -