Relevant bibliographies by topics / Complex semisimple Lie algebra

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  2. Dissertations / Theses
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Academic literature on the topic 'Complex semisimple Lie algebra'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Complex semisimple Lie algebra"

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ARDAKOV, KONSTANTIN, and IAN GROJNOWSKI. "KRULL DIMENSION OF AFFINOID ENVELOPING ALGEBRAS OF SEMISIMPLE LIE ALGEBRAS." Glasgow Mathematical Journal 55, A (2013): 7–26. http://dx.doi.org/10.1017/s0017089513000487.

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AbstractUsing Beilinson–Bernstein localisation, we give another proof of Levasseur's theorem on the Krull dimension of the enveloping algebra of a complex semisimple Lie algebra. The proof also extends to the case of affinoid enveloping algebras.
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ONDRUS, MATTHEW, and EMILIE WIESNER. "WHITTAKER MODULES FOR THE VIRASORO ALGEBRA." Journal of Algebra and Its Applications 08, no. 03 (2009): 363–77. http://dx.doi.org/10.1142/s0219498809003370.

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Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.
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ZHANG, SHOUCHUAN, YAO-ZHONG ZHANG, and HUI-XIANG CHEN. "CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS." Journal of Algebra and Its Applications 06, no. 06 (2007): 919–50. http://dx.doi.org/10.1142/s0219498807002569.

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We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter–Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field k is the complex field and G is a finite abelian group, we classify quiver Hopf algebras over G, multiple Taft algebras over G and Nichols algebras in [Formula: see text]. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.
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Cheung, Wai-Shun, and Tin-Yau Tam. "Star-Shapedness and K-Orbits in Complex Semisimple Lie Algebras." Canadian Mathematical Bulletin 54, no. 1 (2011): 44–55. http://dx.doi.org/10.4153/cmb-2010-097-7.

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AbstractGiven a complex semisimple Lie algebra is a compact real form of g), let be the orthogonal projection (with respect to the Killing form) onto the Cartan subalgebra , where t is a maximal abelian subalgebra of . Given x ∈ g, we consider π(Ad(K)x), where K is the analytic subgroup G corresponding to , and show that it is star-shaped. The result extends a result of Tsing. We also consider the generalized numerical range f (Ad(K)x), where f is a linear functional on g. We establish the star-shapedness of f (Ad(K)x) for simple Lie algebras of type B.
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Reeder, Mark. "Exterior Powers of the Adjoint Representation." Canadian Journal of Mathematics 49, no. 1 (1997): 133–59. http://dx.doi.org/10.4153/cjm-1997-007-1.

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Helmke, Uwe, and Martin Kleinsteuber. "A differential equation for diagonalizing complex semisimple Lie algebra elements." Systems & Control Letters 59, no. 1 (2010): 72–78. http://dx.doi.org/10.1016/j.sysconle.2009.12.001.

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BISWAS, INDRANIL, and PRALAY CHATTERJEE. "ON THE EXACTNESS OF KOSTANT–KIRILLOV FORM AND THE SECOND COHOMOLOGY OF NILPOTENT ORBITS." International Journal of Mathematics 23, no. 08 (2012): 1250086. http://dx.doi.org/10.1142/s0129167x12500863.

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We give a criterion for the Kostant–Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebra.
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Djoković, D. Ž. "On real forms of complex semisimple Lie algebras." Aequationes mathematicae 58, no. 1-2 (1999): 73–84. http://dx.doi.org/10.1007/s000100050008.

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Djoković, D. Ž. "On real forms of complex semisimple Lie algebras." Aequationes Mathematicae 58, no. 1-2 (1999): 73–84. http://dx.doi.org/10.1007/s000100050094.

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BARANOV, A. A., and A. E. ZALESSKII. "PLAIN REPRESENTATIONS OF LIE ALGEBRAS." Journal of the London Mathematical Society 63, no. 3 (2001): 571–91. http://dx.doi.org/10.1017/s0024610701002101.

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In this paper we study representations of finite dimensional Lie algebras. In this case representations are not necessarily completely reducible. As the general problem is known to be of enormous complexity, we restrict ourselves to representations that behave particularly well on Levi subalgebras. We call such representations plain (Definition 1.1). Informally, we show that the theory of plain representations of a given Lie algebra L is equivalent to representation theory of finitely many finite dimensional associative algebras, also non-semisimple. The sense of this is to distinguish represe
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Dissertations / Theses on the topic "Complex semisimple Lie algebra"

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Sawyer, Cameron C. (Cameron Cunningham). "The Cohomology for the Nil Radical of a Complex Semisimple Lie Algebra." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc501116/.

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Let g be a complex semisimple Lie algebra, Vλ an irreducible g-module with high weight λ, pI a standard parabolic subalgebra of g with Levi factor £I and nil radical nI, and H*(nI, Vλ) the cohomology group of Λn'I ⊗Vλ. We describe the decomposition of H*(nI, Vλ) into irreducible £1-modules.
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Tsumura, Hirofumi, and Kohji Matsumoto. "On Witten multiple zeta-functions associated with semisimple Lie algebras I." Annales de L'Institut Fourier, 2006. http://hdl.handle.net/2237/20336.

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Gruson, Caroline. "Sur les super groupes de Lie." Paris 7, 1993. http://www.theses.fr/1993PA077056.

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La première partie est une adaptation au cadre des super groupes de Lie du théorème du à Cartier qui assure que les groupes formels sont lisses en caractérisque zéro. La seconde partie donne une description des super groupes de Lie dits vraiment classiques comme groupes d'automorphismes des super algèbres semi-simples à involution, selon une méthode de Weil. La troisième partie est consacrée à l'étude de l'idéal définissant l'orbite d'un vecteur de plus haut poids d'une représentation simple de dimension finie d'une super algèbre de Lie basique classique complexe.
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To, Kai-ming Simon, and 杜啟明. "On some aspects of a Poisson structure on a complex semisimple Lie group." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B45700333.

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Morigi, Davide. "A combinatorial description of the good Z-gradings of the symplectic Lie algebra." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17108/.

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In this thesis we investigate the concept of good Z-grading of a finite dimensional semisimple Lie algebra over an algebraically closed field of characteristic 0. Throughout the thesis we make use of the theorem of Jacobson Morozov, a fundamental result in the Lie theory. First of all we give a fundamental example of good grading, the Dynkin one. Afterwards we study more in general some properties of the good Z-gradings of a Lie algebra. Finally we give a complete description of the good Z-gradings of the symplectic Lie algebra.
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Caprace, Pierre-Emmanuel. ""Abstract" homomorphisms of split Kac-Moody groups." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210962.

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Cette thèse est consacrée à une classe de groupes, appelés groupes de Kac-Moody, qui généralise de façon naturelle les groupes de Lie semi-simples, ou plus précisément, les groupes algébriques réductifs, dans un contexte infini-dimensionnel. On s'intéresse plus particulièrement au problème d'isomorphismes pour ces groupes, en vue d'obtenir un analogue infini-dimensionnel de la célèbre théorie des homomorphismes 'abstraits' de groupes algébriques simples, due à Armand Borel et Jacques Tits.<p><p>Le problème d'isomorphismes qu'on étudie s'avère être un cas particulier d'un problème plus général,
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Matías, Gutierrez Gonzalo Emanuel. "Estudo de nova fórmula de caracteres para representações de Álgebra de Lie semissimples." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7299.

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Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2016-09-21T11:54:01Z No. of bitstreams: 1 DissGEMG.pdf: 900713 bytes, checksum: 6350d5da67ccdaab208cf7961f1161f6 (MD5)<br>Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-21T12:02:05Z (GMT) No. of bitstreams: 1 DissGEMG.pdf: 900713 bytes, checksum: 6350d5da67ccdaab208cf7961f1161f6 (MD5)<br>Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2016-09-21T12:02:16Z (GMT) No. of bitstreams: 1 DissGEMG.pdf: 900713 bytes, checksum: 6350d5da67ccdaab208cf7961f1161f6 (MD5)<br>Made available in
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Shaddad, Amna. "The classification and dynamics of the momentum polytopes of the SU(3) action on points in the complex projective plane with an application to point vortices." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/the-classification-and-dynamics-of-the-momentum-polytopes-of-the-su3-action-on-points-in-the-complex-projective-plane-with-an-application-to-point-vortices(456a7a49-ef1b-4660-a8e6-8d4cd0791d9d).html.

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We have fully classified the momentum polytopes of the SU(3) action on CP(2)xCP(2) and CP(2)xCP(2) xCP(2), both actions with weighted symplectic forms, and their corresponding transition momentum polytopes. For CP(2)xCP(2) the momentum polytopes are distinct line segments. The action on CP(2)xCP(2) xCP(2), has 9 different momentum polytopes. The vertices of the momentum polytopes of the SU(3) action on CP(2)xCP(2) xCP(2), fall into two categories: definite and indefinite vertices. The reduced space corresponding to momentum map image values at definite vertices is isomorphic to the 2-sphere. W
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Bhattacharya, Subhabrata. "Recognition of Complex Events in Open-source Web-scale Videos: Features, Intermediate Representations and their Temporal Interactions." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5768.

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Recognition of complex events in consumer uploaded Internet videos, captured under real-world settings, has emerged as a challenging area of research across both computer vision and multimedia community. In this dissertation, we present a systematic decomposition of complex events into hierarchical components and make an in-depth analysis of how existing research are being used to cater to various levels of this hierarchy and identify three key stages where we make novel contributions, keeping complex events in focus. These are listed as follows: (a) Extraction of novel semi-global features --
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Bäcklund, Pierre. "Studies on boundary values of eigenfunctions on spaces of constant negative curvature." Doctoral thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8920.

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<p>This thesis consists of two papers on the spectral geometry of locally symmetric spaces of Riemannian and Lorentzian signature. Both works are concerned with the idea of relating analysis on such spaces to structures on their boundaries.</p><p>The first paper is motivated by a conjecture of Patterson on the Selberg zeta function of Kleinian groups. We consider geometrically finite hyperbolic cylinders with non-compact Riemann surfaces of finite area as cross sections. For these cylinders, we present a detailed investigation of the Bunke-Olbrich extension operator under the assumption that t
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Books on the topic "Complex semisimple Lie algebra"

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Serre, Jean-Pierre. Complex Semisimple Lie Algebras. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56884-8.

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Serre, Jean-Pierre. Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7.

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1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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1959-, McGovern William M., ed. Nilpotent orbits in semisimple Lie algebras. Van Nostrand Reinhold, 1993.

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Doran, Robert S., 1937- editor of compilation, Friedman, Greg, 1973- editor of compilation, and Nollet, Scott, 1962- editor of compilation, eds. Hodge theory, complex geometry, and representation theory: NSF-CBMS Regional Conference in Mathematics, June 18, 2012, Texas Christian University, Fort Worth, Texas. American Mathematical Society, 2013.

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A, Rossi Carlo, and European Mathematical Society, eds. Lectures on Duflo isomorphisms in Lie algebra and complex geometry. European Mathematical Society, 2011.

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Benkart, Georgia. Stability in modules for classical lie algebras: A constructive approach. American Mathematical Society, 1990.

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Bernhard, Leeb, and Millson John J. 1946-, eds. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. American Mathematical Society, 2008.

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Kapovich, Michael. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. American Mathematical Society, 2008.

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1944-, Kulish P. P., Manojlovic Nenad 1962-, and Samtleben Henning, eds. Infinite dimensional algebras and quantum integrable systems. Birkhäuser Verlag, 2005.

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Book chapters on the topic "Complex semisimple Lie algebra"

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Serre, Jean-Pierre. "Nilpotent Lie Algebras and Solvable Lie Algebras." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_1.

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Serre, Jean-Pierre. "The Algebra sl2 and Its Representations." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_4.

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Knapp, Anthony W. "Complex Semisimple Lie Algebras." In Lie Groups Beyond an Introduction. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4757-2453-0_2.

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Serre, Jean-Pierre. "Semisimple Lie Algebras (General Theorems)." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_2.

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Serre, Jean-Pierre. "Structure of Semisimple Lie Algebras." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_6.

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Onishchik, Arkadij L., and Ernest B. Vinberg. "Complex Semisimple Lie Groups." In Lie Groups and Algebraic Groups. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74334-4_4.

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Kaneyuki, Soji. "Semisimple Graded Lie Algebras." In Analysis and Geometry on Complex Homogeneous Domains. Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1366-6_9.

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Serre, Jean-Pierre. "Linear Representations of Semisimple Lie Algebras." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_7.

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Serre, Jean-Pierre. "Cartan Subalgebras." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_3.

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Serre, Jean-Pierre. "Root Systems." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_5.

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Conference papers on the topic "Complex semisimple Lie algebra"

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Yanovski, Alexandar B., and Moses C. dos Santos. "Quadratic Casimir Invariants for “Universal” Lie Algebra Extensions." In INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES, INTEGRABILITY AND VECTOR FIELDS. AIP, 2011. http://dx.doi.org/10.1063/1.3567135.

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Salerno, Alessio, and Jorge Angeles. "Robustness and Controllability Analysis for Autonomous Navigation of Two-Wheeled Mobile Robots." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35415.

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This work deals with the robustness and controllability analysis for autonomous navigation of two-wheeled mobile robots. The analysis of controllability of the systems at hand is conducted using both the Kalman rank condition for controllability and the Lie Algebra rank condition. We show that the robots targeted in this work can be controlled using a model for autonomous navigation by means of their dynamics model: kinematics will not be sufficient to completely control these underactuated systems. After having proven that these autonomous robots are small-time locally controllable from every
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