DENSE ORBITS FOR ABELIAN SUBGROUPS OF GL(n, ℂ)

Ayadi, Adlene; Marzougui, Habib

doi:10.1142/9789812772640_0004

Cited by 19 publications

(22 citation statements)

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“…A more precise result is obtained if we use the classification of Abelian subgroups of GL k (C) in [1]: Let η = (k 1 , . .…”

Section: Applicationsmentioning

confidence: 99%

Equivariant Abelian principal bundles on nonsingular toric varieties

Dey¹,

Poddar²

2016

Bulletin des Sciences Mathématiques

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We give a classification of the equivariant principal G-bundles on a nonsingular toric variety when G is a closed Abelian subgroup of GL k (C). We prove that any such bundle splits, that is, admits a reduction of structure group to the intersection of G with a torus. We give an explicit parametrization of the isomorphism classes of such bundles for a large family of G when X is complete.2010 Mathematics Subject Classification. 32L05,14M25.

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“…A more precise result is obtained if we use the classification of Abelian subgroups of GL k (C) in [1]: Let η = (k 1 , . .…”

Section: Applicationsmentioning

confidence: 99%

Equivariant Abelian principal bundles on nonsingular toric varieties

Dey¹,

Poddar²

2016

Bulletin des Sciences Mathématiques

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“…where ϕ (1) is the injective linear map associated to G (1) and η : C n−1 −→ C n−2 is a linear map. Then w (1) .…”

Section: Proof Of Theorem 12 Corollaries 13 and 14mentioning

confidence: 99%

“…where ϕ (1) is the injective linear map associated to G (1) and η : C n−1 −→ C n−2 is a linear map. Then w (1) . The set G (1) is an abelian sub-semigroup of T n−1 (C) and rank(F G (1) ) = n − 2.…”

Section: Proof Of Theorem 12 Corollaries 13 and 14mentioning

confidence: 99%

J-class abelian semigroups of matrices on $$\mathbb{C }^{n}$$ and hypercyclicity

Ayadi

Marzougui

2013

RACSAM

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We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C n using the extended limit sets (the J-sets). Moreover we construct for any n ≥ 2 an abelian semigroup G of GL(n, C) generated by n + 1 diagonal matrices which is locally hypercyclic but not hypercyclic and such that JG(e k ) = C n for every k = 1, . . . , n, where (e1, . . . , en) is the canonical basis of C n . This gives a negative answer to a question raised by Costakis and Manoussos.

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“…So the main aim of this paper is to give an explicit arithmetic way for checking the density of any finitely generated additive subgroup of C n and R n , which may be used in a future algorithm. This criterion can be used as a tool to characterize the density of any orbit given by the natural action of any abelian linear or affine group on K n (see for example, [1], [2], [3] and [4]). …”

Section: Introductionmentioning

confidence: 99%