Large dimensional 1-cohomology

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Authors John N. Bray and Robert A. Wilson.
Title Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups.
Published as Submitted to J. Group Theory.
Availability DVI-format or PDF-format.
Abstract It is known that for finite simple groups it is possible for a faithful absolutely irreducible module to have 1-cohomology of dimension at least 3. However, until now no explicit examples have been found. We present two explicit examples where the dimension is exactly 3. It remains an open question as to whether the dimension can be bigger than 3.

Author John N. Bray.
Title A new family of modules with 2-dimensional 1-cohomology.
Published as Submitted to J. Group Theory.
Availability DVI-format or PDF-format.
Abstract It is known that for finite simple groups it is possible for a faithful absolutely irreducible module to have 1-cohomology of dimension at least 3. However, even faithful absolutely irreducible modules with 2-dimensional 1-cohomology are rare. We exhibit a new infinite family of such modules.

Last updated 27th July 2007
John Nicholas Bray