Crossed Product-Like and Pre-Crystalline Graded Rings
Öinert, Johan; Silvestrov, Sergei (2009). Crossed Product-Like and Pre-Crystalline Graded Rings In . Silvestrov, Sergei; Paal, Eugen; Abramov, Viktor; Stolin, Alexander (Eds.). Generalized Lie Theory in Mathematics, Physics and Beyond, 281 - 296: Springer
Book Chapter
|
Published
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English
Authors:
Öinert, Johan
;
Silvestrov, Sergei
Editors:
Silvestrov, Sergei
;
Paal, Eugen
;
Abramov, Viktor
;
Stolin, Alexander
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
We introduce crossed product-like rings, as a natural generalization of
crystalline graded rings, and describe their basic properties. Furthermore, we prove that for certain pre-crystalline graded rings and every crystalline graded ring A, for which the base subring A_0 is commutative, each non-zero two-sided ideal has a nonzero intersection with C_A(A_0), i.e. the commutant of A_0 in A. We also show that in general this property need not hold for crossed product-like rings.
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