Can I read Actions of Algebraic Groups on the Spectrum of Rational Ideals, II on EtoBox?

Actions of Algebraic Groups on the Spectrum of Rational Ideals, II by Nikolaus Vonessen is a Mathematics article available to read on EtoBox.

What is Actions of Algebraic Groups on the Spectrum of Rational Ideals, II about?

We study rational actions of a linear algebraic group G on an algebra V, and the Ž . Ž induced actions on Rat V , the spectrum of rational ideals of V a subset of Ž . . Spec V which often includes all primitive ideals . This work extends results of Moeglin and Rentschler to prime characteristic, often also relaxing their finiteness assumptions on V. In particular, we relate properties of a rational ideal J and its Ž . Ž . orb, the ideal J : G s F ␥ J . The rational ideals of V containing the orb of ␥ g G Ž . J are precisely those in the Zariski-closure X of the orbit of J in Rat V . The Ž G-stratum of J consists of all rational ideals in X whose orbit is dense in X i.e., . whose orb is equal to the orb of J . We show that the G-stratum of a rational ideal consists of exactly one G-orbit, and that rational ideals are maximal in their strata in a strong sense. These results are useful for studying prime and primitive spectra of certain algebras, cf. recent work by Goodearl and Letzter. We further show that Ž . the orbit of J is open in its closure in Rat V , provided that J is locally closed. Ž . Among other results, we show that the semiprime ideal J : G is Goldie, and we Ž . relate

Who reads Actions of Algebraic Groups on the Spectrum of Rational Ideals, II?

Author

Nikolaus Vonessen

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)

Published

1998

Language

EN

Field

Mathematics (Physical Sciences)