alexa Commutativity and ideals in algebraic crossed products
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Commutativity and ideals in algebraic crossed products

Johan OINERT* and Sergei D. SILVESTROV

Centre for Mathematical Sciences, Lund University, Box 118, SE-22100 Lund, Sweden

*Corresponding Author:
Johan OINERT
Centre for Mathematical Sciences
Lund University, Box 118
SE-22100 Lund
Sweden
E-mails: Johan.Oinert@math.lth.se and Sergei.Silvestrov@math.lth.se
 

Received date: October 15, 2007; Revised date: September 01, 2008



 

Abstract

We investigate properties of commutative subrings and ideals in non-commutative algebraic crossed products for actions by arbitrary groups. A description of the commutant of the coecient subring in the crossed product ring is given. Conditions for commutativity and maximal commutativity of the commutant of the coecient subring are provided in terms of the action as well as in terms of the intersection of ideals in the crossed product ring with the coecient subring, specially taking into account both the case of coecient rings without non-trivial zero-divisors and the case of coecient rings with non-trivial zero-divisors.

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