Abstract
A differential-algebraic geometric analogue of the Dixmier–Moeglin equivalence is articulated, and proven to hold for -groups over the constants. The model theory of differentially closed fields of characteristic zero, in particular the notion of analysability in the constants, plays a central role. As an application it is shown that if is a commutative affine Hopf algebra over a field of characteristic zero, and is an Ore extension to which the Hopf algebra structure extends, then satisfies the classical Dixmier–Moeglin equivalence. Along the way it is shown that all such are Hopf Ore extensions in the sense of Brown et al., “Connected Hopf algebras and iterated Ore extensions”, J. Pure Appl. Algebra 219:6 (2015).
Citation
Jason Bell. Omar León Sánchez. Rahim Moosa. "$D$-groups and the Dixmier–Moeglin equivalence." Algebra Number Theory 12 (2) 343 - 378, 2018. https://doi.org/10.2140/ant.2018.12.343
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