TY - JOUR

T1 - Actions of algebraic groups on the spectrum of rational ideals

AU - Vonessen, Nikolaus

N1 - Funding Information:
* Partially supported by the NSF. Current address: Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812-1032. E-mail address: vonessen@ charlo.math.umt.edu.

PY - 1996/6/1

Y1 - 1996/6/1

N2 - Let k be an algebraically closed field and G a linear algebraic group over k acting rationally on a k-algebra V. Generalizing work of Moeglin and Rentschler in characteristic zero, we study the action of G on the spectrum of rational ideals of V. The main result is the following. Suppose that V is semiprime left Goldie. Let L be a G-stable commutative semisimple subalgebra of the total ring of fractions Q(V) of V such that LG = k · 1L. This occurs, for example, if the zero ideal of V is G-rational and L is the center of Q(V). Then there is, for some closed subgroup H of G, a G-equivariant embedding v of L into Q(G/H) (the algebra of rational functions on G/H) such that Q(G/H) is purely inseparable over v(L). This has applications to the closure of the orbit of a rational ideal.

AB - Let k be an algebraically closed field and G a linear algebraic group over k acting rationally on a k-algebra V. Generalizing work of Moeglin and Rentschler in characteristic zero, we study the action of G on the spectrum of rational ideals of V. The main result is the following. Suppose that V is semiprime left Goldie. Let L be a G-stable commutative semisimple subalgebra of the total ring of fractions Q(V) of V such that LG = k · 1L. This occurs, for example, if the zero ideal of V is G-rational and L is the center of Q(V). Then there is, for some closed subgroup H of G, a G-equivariant embedding v of L into Q(G/H) (the algebra of rational functions on G/H) such that Q(G/H) is purely inseparable over v(L). This has applications to the closure of the orbit of a rational ideal.

UR - http://www.scopus.com/inward/record.url?scp=0030171847&partnerID=8YFLogxK

U2 - 10.1006/jabr.1996.0176

DO - 10.1006/jabr.1996.0176

M3 - Article

AN - SCOPUS:0030171847

SN - 0021-8693

VL - 182

SP - 383

EP - 400

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -