Crossed Product-Like and Pre-Crystalline Graded Rings

Johan Öinert () and Sergei D. Silvestrov ()
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Johan Öinert: Lund Institute of Technology, Lund University, Centre for Mathematical Sciences, Division of Mathematics
Sergei D. Silvestrov: Lund Institute of Technology, Lund University, Centre for Mathematical Sciences, Division of Mathematics

Chapter 24 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 281-296 from Springer

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 A0 is commutative, each non-zero two-sided ideal has a nonzero intersection with C A(A0), i.e. the commutant of A0 in A. We also show that in general this property need not hold for crossed product-like rings.

Date: 2009
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DOI: 10.1007/978-3-540-85332-9_24

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