Relevant bibliographies by topics / Unipotent automorphism

Academic literature on the topic 'Unipotent automorphism'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Unipotent automorphism"

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Varea, V. R., and J. J. Varea. "On Automorphisms and Derivations of a Lie Algebra." Algebra Colloquium 13, no. 01 (March 2006): 119–32. http://dx.doi.org/10.1142/s1005386706000149.

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We study automorphisms and derivations of a Lie algebra L of finite dimension satisfying certain centrality conditions. As a consequence, we obtain that every nilpotent normal subgroup of the automorphism group of L is unipotent for a very large class of Lie algebras. This result extends one of Leger and Luks. We show that the automorphism group of a nilpotent Lie algebra can have trivial center and have yet a unipotent identity component.
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Li, Sichen. "Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic — A remark to a paper of Dinh-Oguiso-Zhang." International Journal of Mathematics 31, no. 08 (June 23, 2020): 2050059. http://dx.doi.org/10.1142/s0129167x20500597.

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Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.
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Lawther, Ross, Martin W. Liebeck, and Gary M. Seitz. "Outer unipotent classes in automorphism groups of simple algebraic groups." Proceedings of the London Mathematical Society 109, no. 3 (March 25, 2014): 553–95. http://dx.doi.org/10.1112/plms/pdu011.

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REGETA, ANDRIY. "CHARACTERIZATION OF n-DIMENSIONAL NORMAL AFFINE SLn-VARIETIES." Transformation Groups 27, no. 1 (March 2022): 271–93. http://dx.doi.org/10.1007/s00031-022-09701-3.

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AbstractWe show that any normal irreducible affine n-dimensional SLn-variety X is determined by its automorphism group seen as an ind-group in the category of normal irreducible affine varieties. In other words, if Y is an irreducible affine normal algebraic variety such that Aut(Y) ≃ Aut(X) as an ind-group, then Y ≃ X as a variety. If we drop the condition of normality on Y , then this statement fails. In case n ≥ 3, the result above holds true if we replace Aut(X) by 𝒰(X), where 𝒰(X) is the subgroup of Aut(X) generated by all one-dimensional unipotent subgroups. In dimension 2 we have some interesting exceptions.
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Waldspurger, J. L. "Le Groupe GLn Tordu, Sur un Corps Fini." Nagoya Mathematical Journal 182 (June 2006): 313–79. http://dx.doi.org/10.1017/s002776300002691x.

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AbstractLet q be a finite field, G = GLn(q), θ be the outer automorphism of G, suitably normalized. Consider the non-connected group G ⋊ {1, θ} and its connected component = Gθ. We know two ways to produce functions on , with complex values and invariant by conjugation by G: on one hand, let π be an irreducible representation of G we can and do extend to a representation π+ of G ⋊ {1, θ}, then the restriction trace to of the character of π+ is such a function; on the other hand, Lusztig define character-sheaves a, whose characteristic functions ϕ(a) are such functions too. We consider only “quadratic-unipotent” representations. For all such representation π, we define a suitable extension π+, a character-sheave f(π) and we prove an identity trace = γ(π)ϕ(f(π)) with an explicit complex number γ(π).
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Barbari, P., and A. Kobotis. "On nilpotent filiform Lie algebras of dimension eight." International Journal of Mathematics and Mathematical Sciences 2003, no. 14 (2003): 879–94. http://dx.doi.org/10.1155/s016117120311201x.

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The aim of this paper is to determine both the Zariski constructible set of characteristically nilpotent filiform Lie algebrasgof dimension8and that of the set of nilpotent filiform Lie algebras whose group of automorphisms consists of unipotent automorphisms, in the variety of filiform Lie algebras of dimension8overC.
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Hanzer, Marcela, and Gordan Savin. "Eisenstein Series Arising from Jordan Algebras." Canadian Journal of Mathematics 72, no. 1 (January 9, 2019): 183–201. http://dx.doi.org/10.4153/cjm-2018-033-2.

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AbstractWe describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.
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Levchuk, V. M. "Automorphisms of unipotent subgroups of chevalley groups." Algebra and Logic 29, no. 3 (May 1990): 211–24. http://dx.doi.org/10.1007/bf01979936.

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Bavula, V. V., and T. H. Lenagan. "Quadratic and cubic invariants of unipotent affine automorphisms." Journal of Algebra 320, no. 12 (December 2008): 4132–55. http://dx.doi.org/10.1016/j.jalgebra.2008.07.029.

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Ginzburg, David. "Certain conjectures relating unipotent orbits to automorphic representations." Israel Journal of Mathematics 151, no. 1 (December 2006): 323–55. http://dx.doi.org/10.1007/bf02777366.

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Dissertations / Theses on the topic "Unipotent automorphism"

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Ye, Lizao. "Faisceau automorphe unipotent pour G₂, nombres de Franel, et stratification de Thom-Boardman." Thesis, Université de Lorraine, 2019. http://www.theses.fr/2019LORR0081/document.

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Dans cette thèse, d’une part, nous généralisons au cas équivariant un résultat de J. Denef et F. Loeser sur les sommes trigonométriques sur un tore ; d’autre part, nous étudions la stratification de Thom-Boardman associée à la multiplication des sections globales des fibrés en droites sur une courbe. Nous montrons une inégalité subtile sur les dimensions de ces strates. Notre motivation vient du programme de Langlands géométrique. En s’appuyant sur les travaux de W. T. Gan, N. Gurevich, D. Jiang et de S. Lysenko, nous proposons, pour le groupe réductif G de type G2, une construction conjecturale du faisceau automorphe dont le paramètre d’Arthur est unipotent et sous-régulier. En utilisant nos deux résultats ci-dessus, nous déterminons les rangs génériques de toutes les composantes isotypiques d’un faisceau S₃-équivariant qui apparaît dans notre conjecture, ce S₃ étant le centralisateur du SL2 sous-régulier dans le groupe dual de Langlands de G
In this thesis, on the one hand, we generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori ; on the other hand, we study the Thom-Boardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group G of type G2, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and sub-regular. Using our two results above, we determine the generic ranks of all isotypic components of an S3-equivaraint sheaf which appears in our conjecture, this S3 being the centraliser of the sub-regular SL2 inside the Langlands dual group of G
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FRATI, MARCO. "Unipotent Automorphisms of Soluble Groups." Doctoral thesis, 2013. http://hdl.handle.net/2158/806278.

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Books on the topic "Unipotent automorphism"

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James, Arthur. Unipotent automorphic representations: Conjectures. Toronto: Dept. of Mathematics, University of Toronto, 1990.

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Book chapters on the topic "Unipotent automorphism"

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Mœglin, Colette. "Stabilite pour les representations elliptiques de reduction unipotente; le cas des groupes unitaires." In Automorphic Representations, L-Functions and Applications: Progress and Prospects, edited by James W. Cogdell, Dihua Jiang, Stephen S. Kudla, David Soudry, and Robert J. Stanton. Berlin, New York: DE GRUYTER, 2005. http://dx.doi.org/10.1515/9783110892703.361.

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