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SUMMARY:Mixed graded structures for the K-theory of Azumaya algebras - Nic
 olas Garrel (University of Alberta)
DTSTART:20200213T111500Z
DTEND:20200213T121500Z
UID:TALK139558@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:If we encode Morita theory for R-algebras as a monoidal catego
 ry where morphisms are bimodules\, then algebraic K-theory becomes a (lax)
  monoidal functor from this category to graded abelian groups. We show tha
 t if we restrict to Azumaya algebras\, strong symmetry properties coming f
 rom the Goldman element allow to coherently lift certain Brauer subgroups 
 to the the level of Morita equivalences\, which gives rise to (graded-)com
 mutative algebras of K-theory\, graded over the corresponding Brauer subgr
 oup. We also study analogue constructions for hermitian K-theory of Azumay
 a algebras with involution<br><br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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