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2 results

  • Embedding the Hopf Automorphism Group into the Brauer Group

  • Fred Van Oystaeyen, Yinhuo Zhang
  • Journal:
    Canadian Mathematical Bulletin / Volume 41 / Issue 3 / 01 September 1998
    Published online by Cambridge University Press:
    20 November 2018, pp. 359-367
    Print publication:
    01 September 1998
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  • Let $H$ be a faithfully projective Hopf algebra over a commutative ring $k$. In [8, 9] we defined the Brauer group $\text{BQ}(k,H)$ of $H$ and an homomorphism $\pi $ from Hopf automorphism group $\text{Au}{{\text{t}}_{\text{Hopf}}}(H)$ to $\text{BQ}(k,H)$. In this paper, we show that the morphism $\pi $ can be embedded into an exact sequence.

  • Division Graded Algebras in the Brauer-Wall Group

  • Francis Coghlan, Peter Hoffman
  • Journal:
    Canadian Mathematical Bulletin / Volume 39 / Issue 1 / 01 March 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 21-24
    Print publication:
    01 March 1996
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  • We show that every element in the Brauer-Wall group of a field with characteristic different from 2 is represented uniquely by a division graded algebra, (i.e. homogeneous elements are invertible) but, of course, not necessarily by a graded (division algebra). This is a fairly direct consequence of Wall's structure theory for central simple Z/2-graded algebras.