On the Brauer Monoid for Finite Fields

Vladimir V. Kirichenko () and Boris V. Novikov ()

A chapter in Finite Fields and Applications, 2001, pp 313-318 from Springer

Abstract: Abstract The definition of the Brauer monoid M(G, L) (G is the Galois group of a field L) was given in [3]. In this article it is studied by the notions of modifications [6] and 0-cohomology [5]. Namely, M(G, L) is a semilattice of Abelian groups each of which is isomorphic to H 0 2 (S, L), the second 0-cohomology of a modification of G. We show that if the subgroup U of the invertible elements of S is normal in S then Ker(H 0 2 (S, L) → H 2(U, L)) is isomorphic to the second 0-cohomology of S/U. In particular, for finite fields the influence of invertible elements of modifications on the Brauer monoid may be eliminated in some sense.

Keywords: Abelian Group; Finite Field; Galois Group; Invertible Element; Finite Dimensional Algebra (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56755-1_24

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DOI: 10.1007/978-3-642-56755-1_24

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