Isotropy in group cohomology

Nir Ben David, Yuval Ginosar, Ehud Meir

Research output: Contribution to journalArticle

3 Citations (Scopus)
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Abstract

The analog of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N?G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N. This yields a method to construct groups of central type from such quotients, known as Involutive Yang?Baxter groups. Another motivation for the search of normal Lagrangians comes from a non-commutative generalization of Heisenberg liftings that require normality.

Although it is true that symplectic forms over finite nilpotent groups always admit Lagrangians, we exhibit an example where none of these subgroups is normal. However, we prove that symplectic forms over nilpotent groups always admit normal Lagrangians if all their p-Sylow subgroups are of order less than p8.
Original languageEnglish
Pages (from-to)587-599
Number of pages13
JournalBulletin of the London Mathematical Society
Volume46
Issue number3
Early online date1 Apr 2014
DOIs
Publication statusPublished - Jun 2014

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Group Cohomology
Isotropy
Symplectic Form
Nilpotent Group
Quotient
Finite Group
Sylow Subgroup
Bijective
Cocycle
One to one correspondence
Normality
Inflation
Subgroup
Analogue

Cite this

Isotropy in group cohomology. / Ben David, Nir; Ginosar, Yuval; Meir, Ehud.

In: Bulletin of the London Mathematical Society, Vol. 46, No. 3, 06.2014, p. 587-599.

Research output: Contribution to journalArticle

Ben David, Nir ; Ginosar, Yuval ; Meir, Ehud. / Isotropy in group cohomology. In: Bulletin of the London Mathematical Society. 2014 ; Vol. 46, No. 3. pp. 587-599.
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