CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

On Valuations, Places and Graded Rings Associated to $*$-Orderings

  Published:2007-03-01
 Printed: Mar 2007
  • Igor Klep
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We study natural $*$-valuations, $*$-places and graded $*$-rings associated with $*$-ordered rings. We prove that the natural $*$-valuation is always quasi-Ore and is even quasi-commutative (\emph{i.e.,} the corresponding graded $*$-ring is commutative), provided the ring contains an imaginary unit. Furthermore, it is proved that the graded $*$-ring is isomorphic to a twisted semigroup algebra. Our results are applied to answer a question of Cimpri\v c regarding $*$-orderability of quantum groups.
Keywords: $*$--orderings, valuations, rings with involution $*$--orderings, valuations, rings with involution
MSC Classifications: 14P10, 16S30, 16W10 show english descriptions Semialgebraic sets and related spaces
Universal enveloping algebras of Lie algebras [See mainly 17B35]
Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
14P10 - Semialgebraic sets and related spaces
16S30 - Universal enveloping algebras of Lie algebras [See mainly 17B35]
16W10 - Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/