Relevant bibliographies by topics / Lie groups

Academic literature on the topic 'Lie groups'

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Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Lie groups"

1

Hiraga, Kaoru. "Lie groups." Duke Mathematical Journal 85, no. 1 (October 1996): 167–81. http://dx.doi.org/10.1215/s0012-7094-96-08507-5.

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Alekseevskii, D. V. "Lie groups." Journal of Soviet Mathematics 28, no. 6 (March 1985): 924–49. http://dx.doi.org/10.1007/bf02105458.

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Ni, Xiang, and Chengming Bai. "Special symplectic Lie groups and hypersymplectic Lie groups." manuscripta mathematica 133, no. 3-4 (June 30, 2010): 373–408. http://dx.doi.org/10.1007/s00229-010-0375-z.

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HOFMANN, K. H., and K. H. NEEB. "Pro-Lie groups which are infinite-dimensional Lie groups." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 2 (March 2009): 351–78. http://dx.doi.org/10.1017/s030500410800128x.

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AbstractA pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups with a smooth exponential function which maps a zero neighbourhood in the Lie algebra diffeomorphically onto an open identity neighbourhood of the group.
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Wüstner, Michael. "Splittable Lie Groups and Lie Algebras." Journal of Algebra 226, no. 1 (April 2000): 202–15. http://dx.doi.org/10.1006/jabr.1999.8162.

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Hofmann, Karl H., Sidney A. Morris, and Markus Stroppel. "Locally compact groups, residual Lie groups, and varieties generated by Lie groups." Topology and its Applications 71, no. 1 (June 1996): 63–91. http://dx.doi.org/10.1016/0166-8641(95)00068-2.

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Howard, Eric. "Theory of groups and symmetries: Finite groups, Lie groups and Lie algebras." Contemporary Physics 60, no. 3 (July 3, 2019): 275. http://dx.doi.org/10.1080/00107514.2019.1663933.

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Pressley, Andrew N. "LIE GROUPS AND ALGEBRAIC GROUPS." Bulletin of the London Mathematical Society 23, no. 6 (November 1991): 612–14. http://dx.doi.org/10.1112/blms/23.6.612b.

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Wojtyński, Wojciech. "Lie groups as quotient groups." Reports on Mathematical Physics 40, no. 2 (October 1997): 373–79. http://dx.doi.org/10.1016/s0034-4877(97)85935-6.

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Doran, C., D. Hestenes, F. Sommen, and N. Van Acker. "Lie groups as spin groups." Journal of Mathematical Physics 34, no. 8 (August 1993): 3642–69. http://dx.doi.org/10.1063/1.530050.

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Dissertations / Theses on the topic "Lie groups"

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Eddy, Scott M. "Lie Groups and Lie Algebras." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1320152161.

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Ahluwalia, Kanwardeep Singh. "Lie bialgebras and Poisson lie groups." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388758.

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pl, tomasz@uci agh edu. "A Lie Group Structure on Strict Groups." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1076.ps.

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Harkins, Andrew. "Combining lattices of soluble lie groups." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341777.

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Öhrnell, Carl. "Lie Groups and PDE." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420706.

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Burroughs, Nigel John. "The quantisation of Lie groups and Lie algebras." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358486.

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Krook, Jonathan. "Overview of Lie Groups and Their Lie Algebras." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-275722.

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Intuitively, Lie groups are groups that are also smooth. The aim of this thesis is to describe how Lie groups are defined as smooth manifolds, and to look into their properties. To each Lie group there exists an associated vector space, which is called the Lie algebra of the Lie group. We will investigate what properties of a Lie group can be derived from its Lie algebra. As an application, we will characterise all unitary irreducible finite dimensional representations of the Lie group SO(3).
Liegrupper kan ses som grupper som även är glatta. Målet med den här rapporten är att definiera Liegrupper som glatta mångfalder, och att undersöka några av liegruppernas egenskaper. Till varje Liegrupp kan man relatera ett vektorrum, som kallas Liegruppens Liealgebra. Vi kommer undersöka vilka egenskaper hos en Liegrupp som kan härledas från dess Liealgebra. Som tillämpning kommer vi karaktärisera alla unitära irreducibla ändligtdimensionella representationer av Liegruppen SO(3).
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Ray, Jishnu. "Iwasawa algebras for p-adic Lie groups and Galois groups." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS189/document.

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Un outil clé dans la théorie des représentations p-adiques est l'algèbre d'Iwasawa, construit par Iwasawa pour étudier les nombres de classes d'une tour de corps de nombres. Pour un nombre premier p, l'algèbre d'Iwasawa d'un groupe de Lie p-adique G, est l'algèbre de groupe G complétée non-commutative. C'est aussi l'algèbre des mesures p-adiques sur G. Les objets provenant de groupes semi-simples, simplement connectés ont des présentations explicites comme la présentation par Serre des algèbres semi-simples et la présentation de groupe de Chevalley par Steinberg. Dans la partie I, nous donnons une description explicite des certaines algèbres d'Iwasawa. Nous trouvons une présentation explicite (par générateurs et relations) de l'algèbre d'Iwasawa pour le sous-groupe de congruence principal de tout groupe de Chevalley semi-simple, scindé et simplement connexe sur Z_p. Nous étendons également la méthode pour l'algèbre d'Iwasawa du sous-groupe pro-p Iwahori de GL (n, Z_p). Motivé par le changement de base entre les algèbres d'Iwasawa sur une extension de Q_p nous étudions les représentations p-adiques globalement analytiques au sens d'Emerton. Nous fournissons également des résultats concernant la représentation de série principale globalement analytique sous l'action du sous-groupe pro-p Iwahori de GL (n, Z_p) et déterminons la condition d'irréductibilité. Dans la partie II, nous faisons des expériences numériques en utilisant SAGE pour confirmer heuristiquement la conjecture de Greenberg sur la p-rationalité affirmant l'existence de corps de nombres "p-rationnels" ayant des groupes de Galois (Z/2Z)^t. Les corps p-rationnels sont des corps de nombres algébriques dont la cohomologie galoisienne est particulièrement simple. Ils sont utilisés pour construire des représentations galoisiennes ayant des images ouvertes. En généralisant le travail de Greenberg, nous construisons de nouvelles représentations galoisiennes du groupe de Galois absolu de Q ayant des images ouvertes dans des groupes réductifs sur Z_p (ex GL (n, Z_p), SL (n, Z_p ), SO (n, Z_p), Sp (2n, Z_p)). Nous prouvons des résultats qui montrent l'existence d'extensions de Lie p-adiques de Q où le groupe de Galois correspond à une certaine algèbre de Lie p-adique (par exemple sl(n), so(n), sp(2n)). Cela répond au problème classique de Galois inverse pour l'algèbre de Lie simple p-adique
A key tool in p-adic representation theory is the Iwasawa algebra, originally constructed by Iwasawa in 1960's to study the class groups of number fields. Since then, it appeared in varied settings such as Lazard's work on p-adic Lie groups and Fontaine's work on local Galois representations. For a prime p, the Iwasawa algebra of a p-adic Lie group G, is a non-commutative completed group algebra of G which is also the algebra of p-adic measures on G. It is a general principle that objects coming from semi-simple, simply connected (split) groups have explicit presentations like Serre's presentation of semi-simple algebras and Steinberg's presentation of Chevalley groups as noticed by Clozel. In Part I, we lay the foundation by giving an explicit description of certain Iwasawa algebras. We first find an explicit presentation (by generators and relations) of the Iwasawa algebra for the principal congruence subgroup of any semi-simple, simply connected Chevalley group over Z_p. Furthermore, we extend the method to give a set of generators and relations for the Iwasawa algebra of the pro-p Iwahori subgroup of GL(n,Z_p). The base change map between the Iwasawa algebras over an extension of Q_p motivates us to study the globally analytic p-adic representations following Emerton's work. We also provide results concerning the globally analytic induced principal series representation under the action of the pro-p Iwahori subgroup of GL(n,Z_p) and determine its condition of irreducibility. In Part II, we do numerical experiments using a computer algebra system SAGE which give heuristic support to Greenberg's p-rationality conjecture affirming the existence of "p-rational" number fields with Galois groups (Z/2Z)^t. The p-rational fields are algebraic number fields whose Galois cohomology is particularly simple and they offer ways of constructing Galois representations with big open images. We go beyond Greenberg's work and construct new Galois representations of the absolute Galois group of Q with big open images in reductive groups over Z_p (ex. GL(n, Z_p), SL(n, Z_p), SO(n, Z_p), Sp(2n, Z_p)). We are proving results which show the existence of p-adic Lie extensions of Q where the Galois group corresponds to a certain specific p-adic Lie algebra (ex. sl(n), so(n), sp(2n)). This relates our work with a more general and classical inverse Galois problem for p-adic Lie extensions
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Jimenez, William. "Riemannian submersions and Lie groups." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2648.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.
Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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Books on the topic "Lie groups"

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Duistermaat, J. J. Lie groups. Berlin: Springer, 2000.

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Duistermaat, J. J., and J. A. C. Kolk. Lie Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-56936-4.

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Bump, Daniel. Lie Groups. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2.

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Bump, Daniel. Lie Groups. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3.

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San Martin, Luiz A. B. Lie Groups. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7.

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Bourbaki, Nicolas. Lie Groups and Lie Algebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-89394-3.

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Komrakov, B. P., I. S. Krasil’shchik, G. L. Litvinov, and A. B. Sossinsky, eds. Lie Groups and Lie Algebras. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5258-7.

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Serre, Jean-Pierre. Lie Algebras and Lie Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-540-70634-2.

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Bourbaki, Nicolas. Lie groups and Lie algebras. Berlin: Springer, 2004.

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Nicolas Bourbaki. Lie groups and Lie algebras. Berlin: Springer-Verlag, 1989.

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Book chapters on the topic "Lie groups"

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Duistermaat, J. J., and J. A. C. Kolk. "Lie Groups and Lie Algebras." In Lie Groups, 1–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-56936-4_1.

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San Martin, Luiz A. B. "Lie Groups and Lie Algebras." In Lie Groups, 87–116. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7_5.

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Jeevanjee, Nadir. "Groups, Lie Groups, and Lie Algebras." In An Introduction to Tensors and Group Theory for Physicists, 109–86. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-14794-9_4.

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Jeevanjee, Nadir. "Groups, Lie Groups, and Lie Algebras." In An Introduction to Tensors and Group Theory for Physicists, 87–143. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-4715-5_4.

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Onishchik, Arkadij L., and Ernest B. Vinberg. "Lie Groups." In Lie Groups and Algebraic Groups, 1–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-74334-4_1.

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Baker, Andrew. "Lie Groups." In Springer Undergraduate Mathematics Series, 181–209. London: Springer London, 2002. http://dx.doi.org/10.1007/978-1-4471-0183-3_7.

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Sontz, Stephen Bruce. "Lie Groups." In Universitext, 93–103. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14765-9_7.

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Schneider, Peter. "Lie Groups." In Grundlehren der mathematischen Wissenschaften, 89–153. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21147-8_3.

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Selig, J. M. "Lie Groups." In Monographs in Computer Science, 9–24. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-2484-4_2.

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Rudolph, Gerd, and Matthias Schmidt. "Lie Groups." In Theoretical and Mathematical Physics, 219–67. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5345-7_5.

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Conference papers on the topic "Lie groups"

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Sarlette, Alain, Silvere Bonnabel, and Rodolphe Sepulchre. "Coordination on Lie groups." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4739201.

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Galaviz, Imelda. "Introductory Lectures on Lie Groups and Lie Algebras." In ADVANCED SUMMER SCHOOL IN PHYSICS 2005: Frontiers in Contemporary Physics EAV05. AIP, 2006. http://dx.doi.org/10.1063/1.2160969.

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Kawazoe, T., T. Oshima, and S. Sano. "Representation Theory of Lie Groups and Lie Algebras." In Fuji-Kawaguchiko Conference on Representation Theory of Lie Groups and Lie Algebras. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814537162.

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Chauchat, Paul, Axel Barrau, and Silvere Bonnabel. "Invariant smoothing on Lie Groups." In 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2018. http://dx.doi.org/10.1109/iros.2018.8594068.

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Aguilar, M. A. "Lie groups and differential geometry." In The XXX Latin American school of physics ELAF: Group theory and its applications. AIP, 1996. http://dx.doi.org/10.1063/1.50217.

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Satici, Aykut C., and Mark W. Spong. "Connectivity control on Lie groups." In 2013 9th Asian Control Conference (ASCC). IEEE, 2013. http://dx.doi.org/10.1109/ascc.2013.6606252.

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Kun, Gabor. "Differential games on Lie groups." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7075873.

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Akter, Sharmin, Md Monirul Islam, Md Rokunojjaman, and Salma Nasrin. "Operations of Lie Groups and Lie Algebras on Manifolds." In 2021 International Conference on Science & Contemporary Technologies (ICSCT). IEEE, 2021. http://dx.doi.org/10.1109/icsct53883.2021.9642569.

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MAKARENKO, N. YU. "GROUPS AND LIE RINGS WITH FROBENIUS GROUPS OF AUTOMORPHISMS." In Proceedings of the Conference. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814350051_0017.

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Gomez, X., and S. Majid. "Relating quantum and braided Lie algebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-6.

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Reports on the topic "Lie groups"

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Arvanitoyeorgos, Andreas. Lie Transformation Groups and Geometry. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-11-35.

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Axford, R. A. Construction of Difference Equations Using Lie Groups. Office of Scientific and Technical Information (OSTI), August 1998. http://dx.doi.org/10.2172/1172.

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Gilmore, Robert. Relations Among Low-dimensional Simple Lie Groups. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-28-2012-1-45.

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Clubok, Kenneth Sherman. Conformal field theory on affine Lie groups. Office of Scientific and Technical Information (OSTI), April 1996. http://dx.doi.org/10.2172/260974.

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Krishnaprasad, P. S., and Dimitris P. Tsakiris. G-Snakes: Nonholonomic Kinematic Chains on Lie Groups. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada453004.

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Cohen, Frederick R., Mentor Stafa, and V. Reiner. On Spaces of Commuting Elements in Lie Groups. Fort Belvoir, VA: Defense Technical Information Center, February 2014. http://dx.doi.org/10.21236/ada606720.

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McHardy, James David, Elias Davis Clark, Joseph H. Schmidt, and Scott D. Ramsey. Lie groups of variable cross-section channel flow. Office of Scientific and Technical Information (OSTI), May 2019. http://dx.doi.org/10.2172/1523203.

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Schmid, Rudolf. Infinite Dimentional Lie Groups With Applications to Mathematical Physics. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-1-2004-54-120.

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Ikawa, Osamu. Motion of Charged Particles in Two-Step Nilpotent Lie Groups. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-252-262.

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Bernatska, Julia. Geometry and Topology of Coadjoint Orbits of Semisimple Lie Groups. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-146-166.

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