English

Affine quotients of supergroups

Representation Theory 2008-09-23 v2 Quantum Algebra

Abstract

In this article we consider sheaf quotients of affine superschemes by affine supergroups that act on them freely. The necessary and sufficient conditions for such quotients to be affine are given. If GG is an affine supergroup and HH is its normal supersubgroup, then we prove that a dur KK-sheaf G/H~~\tilde{\tilde{G/H}} is again affine supergroup. Additionally, if GG is algebraic, then a KK-sheaf G/H~\tilde{G/H} is also algebraic supergroup and it coincides with G/H~~\tilde{\tilde{G/H}}. In particular, any normal supersubgroup of an affine supergroup is faithfully exact.

Keywords

Cite

@article{arxiv.0804.3493,
  title  = {Affine quotients of supergroups},
  author = {A. N. Zubkov},
  journal= {arXiv preprint arXiv:0804.3493},
  year   = {2008}
}

Comments

31 pages

R2 v1 2026-06-21T10:33:28.186Z