Algorithmic testing for dense orbits of Borel subgroups

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Algorithmic testing for dense orbits of Borel subgroups. / Goodwin, Simon.

In: Journal of Pure and Applied Algebra, Vol. 197, No. 1-3, 01.05.2005, p. 171-181.

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@article{3dde466264b3497898cacf0bf8de1da5,
title = "Algorithmic testing for dense orbits of Borel subgroups",
abstract = "Let G be a reductive algebraic group, B a Borel subgroup of G and U the unipotent radical of B. Let it = Lie(U) be the Lie algebra of U and it a B-submodule of it. In this note we discuss the algorithm Dense Orbits of Borel Subgroups (DOOBS) which determines whether B acts on it with a dense orbit. We have programmed DOOBS in GAP4 and used it to classify all instances when B acts on it with a dense orbit for G of sermisimple rank at most 8 and char k zero or good for G. So in particular, we have the classification for G of exceptional type. © 2004 Elsevier B.V. All rights reserved.",
author = "Simon Goodwin",
year = "2005",
month = may,
day = "1",
doi = "10.1016/j.jpaa.2004.08.038",
language = "English",
volume = "197",
pages = "171--181",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "1-3",

}

RIS

TY - JOUR

T1 - Algorithmic testing for dense orbits of Borel subgroups

AU - Goodwin, Simon

PY - 2005/5/1

Y1 - 2005/5/1

N2 - Let G be a reductive algebraic group, B a Borel subgroup of G and U the unipotent radical of B. Let it = Lie(U) be the Lie algebra of U and it a B-submodule of it. In this note we discuss the algorithm Dense Orbits of Borel Subgroups (DOOBS) which determines whether B acts on it with a dense orbit. We have programmed DOOBS in GAP4 and used it to classify all instances when B acts on it with a dense orbit for G of sermisimple rank at most 8 and char k zero or good for G. So in particular, we have the classification for G of exceptional type. © 2004 Elsevier B.V. All rights reserved.

AB - Let G be a reductive algebraic group, B a Borel subgroup of G and U the unipotent radical of B. Let it = Lie(U) be the Lie algebra of U and it a B-submodule of it. In this note we discuss the algorithm Dense Orbits of Borel Subgroups (DOOBS) which determines whether B acts on it with a dense orbit. We have programmed DOOBS in GAP4 and used it to classify all instances when B acts on it with a dense orbit for G of sermisimple rank at most 8 and char k zero or good for G. So in particular, we have the classification for G of exceptional type. © 2004 Elsevier B.V. All rights reserved.

UR - http://www.scopus.com/inward/record.url?scp=14744287318&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2004.08.038

DO - 10.1016/j.jpaa.2004.08.038

M3 - Article

VL - 197

SP - 171

EP - 181

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 1-3

ER -