Affine Quotients of Supergroups
By Alexandr N. Zubkov. 2008
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In this paper 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 G is an affine supergroup and H is its normal supersubgroup, then we prove that a dur K-sheaf $ \mathop {G/H}\limits^ \approx $ is again an affine supergroup. Additionally, if G is algebraic, then a K-sheaf $ \mathop {G/H}\limits^ \sim $ is also an algebraic supergroup and it coincides with $ \mathop {G/H}\limits^ \approx $. In particular, any normal supersubgroup of an affine supergroup is faithfully exact.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ccbe32d7ad0a1621e0c8cb018ca074b31a3c3980
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field (2011, background): “See [17], [28], [29] for recent characteristic-free studies of supergroup schemes.”