Automorphisms and real structures for a Π-symmetric super-Grassmannian

Elizaveta Vishnyakova*, Mikhail Borovoi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Any complex-analytic vector bundle E admits naturally defined homotheties ϕα, α∈C, i.e. ϕα is the multiplication of a local section by a complex number α. We investigate the question when such automorphisms can be lifted to a non-split supermanifold corresponding to E. Further, we compute the automorphism supergroup of a Π-symmetric super-Grassmannian ΠGrn,k, and, using Galois cohomology, we classify the real structures on ΠGrn,k and compute the corresponding supermanifolds of real points.

Original languageEnglish
Pages (from-to)232-286
Number of pages55
JournalJournal of Algebra
StatePublished - 15 Apr 2024


FundersFunder number
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Fundação de Amparo à Pesquisa do Estado de Minas GeraisAPQ-01999-18, RED-00133-21
Universität zu Köln


    • Automorphism supergroup
    • Real structure
    • Super-Grassmannian


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