Relevant bibliographies by topics / Lie algebras

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Lie algebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Lie algebras"

1

Gao, Yongcun, and Daoji Meng. "Affine Lie Algebra Modules and Complete Lie Algebras." Algebra Colloquium 13, no. 03 (September 2006): 481–86. http://dx.doi.org/10.1142/s1005386706000423.

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In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.
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Burde, Dietrich. "LIE ALGEBRA PREDERIVATIONS AND STRONGLY NILPOTENT LIE ALGEBRAS." Communications in Algebra 30, no. 7 (August 7, 2002): 3157–75. http://dx.doi.org/10.1081/agb-120004482.

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Burde, Dietrich, Christof Ender, and Wolfgang Alexander Moens. "Post-Lie algebra structures for nilpotent Lie algebras." International Journal of Algebra and Computation 28, no. 05 (August 2018): 915–33. http://dx.doi.org/10.1142/s0218196718500406.

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We study post-Lie algebra structures on [Formula: see text] for nilpotent Lie algebras. First, we show that if [Formula: see text] is nilpotent such that [Formula: see text], then also [Formula: see text] must be nilpotent, of bounded class. For post-Lie algebra structures [Formula: see text] on pairs of [Formula: see text]-step nilpotent Lie algebras [Formula: see text] we give necessary and sufficient conditions such that [Formula: see text] defines a CPA-structure on [Formula: see text], or on [Formula: see text]. As a corollary, we obtain that every LR-structure on a Heisenberg Lie algebra of dimension [Formula: see text] is complete. Finally, we classify all post-Lie algebra structures on [Formula: see text] for [Formula: see text], where [Formula: see text] is the three-dimensional Heisenberg Lie algebra.
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Burde, Dietrich, and Wolfgang Alexander Moens. "Commutative post-Lie algebra structures on Lie algebras." Journal of Algebra 467 (December 2016): 183–201. http://dx.doi.org/10.1016/j.jalgebra.2016.07.030.

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Burde, Dietrich, and Christof Ender. "Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras." Linear Algebra and its Applications 584 (January 2020): 107–26. http://dx.doi.org/10.1016/j.laa.2019.09.010.

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Li, Haisheng, Shaobin Tan, and Qing Wang. "Trigonometric Lie algebras, affine Lie algebras, and vertex algebras." Advances in Mathematics 363 (March 2020): 106985. http://dx.doi.org/10.1016/j.aim.2020.106985.

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Towers, David A., and Vicente R. Varea. "Elementary Lie algebras and Lie A-algebras." Journal of Algebra 312, no. 2 (June 2007): 891–901. http://dx.doi.org/10.1016/j.jalgebra.2006.11.034.

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Wu, Linli, Mengping Wang, and Yongsheng Cheng. "Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices." Advances in Mathematical Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/6128102.

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Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras g. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ⋉ad⁎ g⁎ and the induced left-symmetry algebra structures on g.
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Jurisich, Elizabeth. "Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra." Journal of Pure and Applied Algebra 126, no. 1-3 (April 1998): 233–66. http://dx.doi.org/10.1016/s0022-4049(96)00142-9.

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Azam, Saeid. "Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori." Canadian Journal of Mathematics 58, no. 2 (April 1, 2006): 225–48. http://dx.doi.org/10.4153/cjm-2006-009-8.

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AbstractWe investigate a class of Lie algebras which we call generalized reductive Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac–Moody Lie algebras. A generalized reductive Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras has been under intensive investigation in recent years. They have also been called extended affine Lie algebras. The larger class of generalized reductive Lie algebras has not been so intensively investigated. We study themin this paper and note that one way they arise is as fixed point subalgebras of finite order automorphisms. We show that the core modulo the center of a generalized reductive Lie algebra is a direct sum of centerless Lie tori. Therefore one can use the results known about the classification of centerless Lie tori to classify the cores modulo centers of generalized reductive Lie algebras.
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Dissertations / Theses on the topic "Lie algebras"

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Yang, Qunfeng. "Some graded Lie algebra structures associated with Lie algebras and Lie algebroids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0007/NQ41350.pdf.

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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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Traustason, Gunnar. "Engel Lie algebras." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334292.

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Ben, Abdeljelil Amine. "Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7743.

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We generalize the results of Leger and Luks and other researchers about generalized derivations to the cases of ternary Lie algebras and n-BiHom Lie algebras. We investigate the derivations algebras of ternary Lie algebras induced from Lie algebras, we explore the subalgebra of quasi-derivations and give their properties. Moreover, we give a classification of the derivations algebras for low dimensional ternary Lie algebras. For the class of n-BiHom Lie algebras, we study the algebras of generalized derivations and prove that the algebra of quasi-derivations can be embedded in the derivation algebra of a larger n-BiHom Lie algebra.
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Bucicovschi, Orest. "Simple Lie algebras, algebraic prolongations and contact structures." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p3307120.

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Thesis (Ph. D.)--University of California, San Diego, 2008.
Title from first page of PDF file (viewed July 1, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 82-85).
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Ammar, Gregory, Christian Mehl, and Volker Mehrmann. "Schur-Like Forms for Matrix Lie Groups, Lie Algebras and Jordan Algebras." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501032.

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We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in intersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry.
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Pinzon, Daniel F. "VERTEX ALGEBRAS AND STRONGLY HOMOTOPY LIE ALGEBRAS." UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/382.

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Vertex algebras and strongly homotopy Lie algebras (SHLA) are extensively used in qunatum field theory and string theory. Recently, it was shown that a Courant algebroid can be naturally lifted to a SHLA. The 0-product in the de Rham chiral algebra has an identical formula to the Courant bracket of vector fields and 1-forms. We show that in general, a vertex algebra has an SHLA structure and that the de Rham chiral algebra has a non-zero l4 homotopy.
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Williams, Michael Peretzian. "Nilpotent N-Lie Algebras." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-02162004-083708/.

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In 1986, Kasymov introduced the concept of nilpotent $n$-Lie algebras, proved an analogue of Engel's Theorem and later proved an analog of Jacobson's refinement of Engel's Theorem. Despite these achievements, the subject of nilpotency in $n$-Lie algebras has not been examined in great detail in the literature since. We shall explore the concept of nilpotent $n$-Lie algebras by examining, and proving where possible, other classical nilpotent group theory and nilpotent Lie algebra results, in the $n$-Lie algebra setting.
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Levene, Rupert Howard. "Lie semigroup operator algebras." Thesis, Lancaster University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421841.

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Frisk, Anders. "On Stratified Algebras and Lie Superalgebras." Doctoral thesis, Uppsala : Department of Mathematics, Uppsala university, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7781.

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Books on the topic "Lie algebras"

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Tauvel, Patrice, and Rupert W. T. Yu. Lie Algebras and Algebraic Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/b139060.

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Tauvel, Patrice. Lie algebras and algebraic groups. Berlin: Springer Berlin, 2010.

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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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Akram, Muhammad. Fuzzy Lie Algebras. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-3221-0.

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Goze, Michel, and Yusupdjan Khakimdjanov. Nilpotent Lie Algebras. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2432-6.

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Fuchs, Dmitry, ed. Unconventional Lie Algebras. Providence, Rhode Island: American Mathematical Society, 1993. http://dx.doi.org/10.1090/advsov/017.

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Book chapters on the topic "Lie algebras"

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Woit, Peter. "Lie Algebras and Lie Algebra Representations." In Quantum Theory, Groups and Representations, 55–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64612-1_5.

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Adler, Mark, Pierre van Moerbeke, and Pol Vanhaecke. "Lie Algebras." In Algebraic Integrability, Painlevé Geometry and Lie Algebras, 7–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05650-9_2.

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Fässler, Albert, and Eduard Stiefel. "Lie Algebras." In Group Theoretical Methods and Their Applications, 181–208. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0395-7_7.

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Menini, Laura, and Antonio Tornambè. "Lie Algebras." In Symmetries and Semi-invariants in the Analysis of Nonlinear Systems, 221–73. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-612-2_6.

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Hall, Brian C. "Lie Algebras." In Graduate Texts in Mathematics, 49–75. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-13467-3_3.

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Bahturin, Yuri. "Lie Algebras." In Basic Structures of Modern Algebra, 199–243. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0839-5_5.

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Pfeifer, Walter. "Lie algebras." In The Lie Algebras su(N), 1–14. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8097-8_1.

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Choie, YoungJu, and Min Ho Lee. "Lie Algebras." In Springer Monographs in Mathematics, 77–89. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29123-5_4.

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Tapp, Kristopher. "Lie algebras." In The Student Mathematical Library, 67–78. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/stml/029/06.

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Dixmier, Jacques. "Lie algebras." In Graduate Studies in Mathematics, 1–65. Providence, Rhode Island: American Mathematical Society, 1996. http://dx.doi.org/10.1090/gsm/011/01.

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Conference papers on the topic "Lie algebras"

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KUBO, F. "COMPATIBLE ALGEBRA STRUCTURES OF LIE ALGEBRAS." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0020.

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Nash, Oliver. "Formalising lie algebras." In CPP '22: 11th ACM SIGPLAN International Conference on Certified Programs and Proofs. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3497775.3503672.

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Kumar, Harshat, Alejandro Parada-Mayorga, and Alejandro Ribeiro. "Algebraic Convolutional Filters on Lie Group Algebras." In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. http://dx.doi.org/10.1109/icassp49357.2023.10095164.

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Gubarev, Vsevolod. "Embedding of post-Lie algebras into postassociative algebras." In 3rd International Congress in Algebras and Combinatorics (ICAC2017). WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811215476_0007.

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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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Iachello, F. "Graded Lie algebras and applications." In LATIN-AMERICAN SCHOOL OF PHYSICS XXXV ELAF; Supersymmetries in Physics and Its Applications. AIP, 2004. http://dx.doi.org/10.1063/1.1853199.

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Bayro-Corrochano, E., and J. Ortegon-Aguilar. "Temphatle tracking with lie algebras." In IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004. IEEE, 2004. http://dx.doi.org/10.1109/robot.2004.1302540.

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Roytenberg, Dmitry, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmeier, and Theodore Voronov. "On weak Lie 2-algebras." In XXVI INTERNATIONAL WORKSHOP ON GEOMETRICAL METHODS IN PHYSICS. AIP, 2007. http://dx.doi.org/10.1063/1.2820967.

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Smirnov, Yu F. "Projection operators for Lie algebras, duperalgebras, and quantum algebras." In The XXX Latin American school of physics ELAF: Group theory and its applications. AIP, 1996. http://dx.doi.org/10.1063/1.50219.

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Reports on the topic "Lie algebras"

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Vilasi, Gaetano. Nambu Dynamics, n-Lie Algebras and Integrability. GIQ, 2012. http://dx.doi.org/10.7546/giq-10-2009-265-278.

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Vilasi, Gaetano. Nambu Dynamics, n-Lie Algebras and Integrability. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-16-2009-77-91.

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Yanovski, Alexander. Compatible Poisson Tensors Related to Bundles of Lie Algebras. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-307-319.

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Tanasa, Adrian, and A'ngel Ballesteros. Solutions for the Constant Quantum Yang-Baxter Equation From Lie (Super) Algebras. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-10-2007-83-92.

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Berceanu, Stefan. A Holomorphic Representation of the Semidirect Sum of Symplectic and Heisenberg Lie Algebras. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-5-2006-5-13.

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Hrivnak, Jiri Hrivnak. Associated Lie Algebras and Graded Contractions of the Pauli Graded sl(3,C). Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-6-2006-47-54.

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Gerdjikov, Vladimir, and Georgi Grahovski. Second Order Reductions of N-Wave Interactions Related to Low-rank Simple Lie Algebras. GIQ, 2012. http://dx.doi.org/10.7546/giq-1-2000-55-77.

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Manev, Hristo. Almost Hypercomplex Manifolds with Hermitian‒Norden Metrics and 4‑dimensional Indecomposable Real Lie Algebras Depending on Two Parameters. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2020. http://dx.doi.org/10.7546/crabs.2020.05.01.

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Slawianowski, Jan J., Vasyl Kovalchuk, Agnieszka Martens, and Barbara Golubowska. Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mehanics on Lie Groups and Meyhods of Group Algebras. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-22-2011-67-94.

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Neeb, Karl-Hermann. Lie Algebra Extensions and Higher Order Cocycles. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-5-2006-48-74.

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