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Topic: Lie, Sophus

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	Lie, Marius Sophus (Site not responding. Last check: 2007-11-06)
		Lie was born near Bergen and studied at Christiania (now Oslo) and abroad at Berlin and Paris.
		This led him to the discovery of Lie groups, one of the basic notions of which is that of infinitesimal transformation.
		The Lie integration theorem, which he developed, made it possible to classify partial differential equations in such a way as to make most of the classical methods of solving such equations reducible to a single principle.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/L/Lie/1.html (207 words)

	Lie (Site not responding. Last check: 2007-11-06)
		Sophus first attended school in the town of Moss, which is a port in south-eastern Norway, on the eastern side of the Oslo Fjord.
		Lie and Klein had quite different characters as humans and mathematicians: the algebraist Klein was fascinated by the peculiarities of charming problems; the analyst Lie, parting from special cases, sought to understand a problem in its appropriate generalisation.
		Certainly Lie was an angry man but he was attacking someone holding such a leading role on the world scene of mathematics that the attack was always more likely to rebound on Lie rather than hurt Klein.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Lie.html (2678 words)

	Lie group (Site not responding. Last check: 2007-11-06)
		In mathematics, a Lie group (pronounced "lee", named after Sophus Lie) is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps.
		Lie groups are important in mathematical analysis, physics and geometry because they serve to describe the symmetry of analytical structures.
		If we require that the Lie group be simply connected, then the global structure is determined by its Lie algebra: for every finite dimensional Lie algebra g over F there is a unique (up to isomorphism) simply connected Lie group G with g as Lie algebra.
	www.sciencedaily.com /encyclopedia/lie_group (1429 words)

	Sophus Lie - Wikipedia, the free encyclopedia
		Marius Sophus Lie (December 17, 1842 - February 18, 1899) was a Norwegian-born mathematician who largely created the theory of continuous symmetry, and applied it to the study of geometric structures and differential equations.
		Lie's principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called Lie groups) could be better understood by "linearizing" them, and studying the corresponding generating vector fields (the so-called infinitesimal generators).
		The generators obey a linearized version of the group law called the commutator bracket, and have the structure of what we today, in honour of Lie, call a Lie algebra.
	en.wikipedia.org /wiki/Sophus_Lie (136 words)

	biog Lie
		Lie had started examining partial differential equations, hoping that he could find a theory which was analogous to Galois' theory of equations.
		This led Lie to define what he called a continuous transformation group, but which is not a group according to our definition, rather what is today called a Lie algebra.
		Lie returned to Kristiania in 1898 to take up a post specially created for him but his health was already deteriorating and he died soon after taking up the post, on February 18, 1899.
	www.math.uit.no /seminar/Lie_biog.htm (975 words)

	LIE
		Lie wrote a short mathematical paper in 1869, which he published at his own expense.
		It was during the winter of 1873-74 that Lie began to develop systematically what became his theory of continuous transformation groups, later called Lie Groups leaving behind his original intention of examining partial differential equations.
		He did this quite independently of Lie (and not it would appear in a manner which Lie found satisfactory), and it was Cartan who completed the classification of semi-simple Lie algebras in 1900.
	www.algana.co.uk /FamousNames/L/lie.htm (542 words)

	Geometry.Net - Pure_And_Applied_Math: Lie Algebra
		lie algebra Root, The roots of a semisimple Liealgebra are the lie algebra weights occurring in its adjoint representation.
		The Lie algebra simple roots are the positive roots which cannot be written as a sum of positive roots.
		A lie algebra over a field is a vectorspace with a bilinear map, called the Lie bracket and denoted.
	www.988.com /pure_and_applied_math/lie_algebra.html (1651 words)

	Lie groups and Lie Algebras (Site not responding. Last check: 2007-11-06)
		AMCA: Lie Groups and Lie Algebras Acting on Surfaces by Morris W. Hirsch...
		Lie Groups, Lie Algebras and Symmetries of Differential...
		MTH 914 Lie Groups and Lie Algebras I F03 8/25/03...
	www.scienceoxygen.com /math/605.html (195 words)

	Lie derivative
		Sophus Lie is noted for his contributions to the theories of differential equations and continuous transformation groups.
		Lie derivative is introduced in Bishop and Goldberg "Tensor Analysis on Manifolds" on p.
		The idea that Cartan's formula for the Lie derivative acting on forms yields the functional format for the Lorentz force as a component of the Lie derivative is mathematically correct.
	quantumfuture.net /quantum_future/lie.htm (8445 words)

	Read This: The Mathematician Sophus Lie
		Lie belonged to three over-lapping groups: he was an increasingly eminent Norwegian man of Science, he belonged to the mathematical communities of Norway and of Leipzig, and he belonged to the international community of mathematicians.
		The oft-told tale that Lie swung his style over from geometry to analysis in order to be understood by the heavyweights in Berlin is neither confirmed nor denied here, but left unexplored.
		Lie is famous for having some sort of nervous breakdown in 1889.
	www.maa.org /reviews/audacity.html (1068 words)

	Learn about Lie group. Complete listing of Lie group. Lie group in Smartpedia Online (Site not responding. Last check: 2007-11-06)
		Lie algebra which completely captures the local structure of the group, at least if the Lie group is connected.
		Lie algebra associated with G, usually denoted by a Gothic g.
		It turns out that this bilinear operation satisfies the axioms of a Lie bracket, and it is equal to the one defined through left-invariant vector fields.
	www.smartpedia.com /s/b/Lie_group (1517 words)

	Amazon.ca: Books: The Mathematician Sophus Lie: It Was the Audacity of My Thinking (Site not responding. Last check: 2007-11-06)
		Sophus Lie (1842-1899) is without doubt one of Norway's greatest scientific talents.
		The terms Lie groups and Lie algebra are today part of the standard mathematical vocabulary.
		The academic and scientific career brought Lie from Christiania to Leipzig as professor, before the attempt to call him back to Norway, when she stood on the threshhold to national sovereignty, was successful.
	www.amazon.ca /exec/obidos/ASIN/3540421378 (290 words)

	Lie, Marius Sophus (1842-1899)
		Lie discovered the contact transformation, which maps curves into surfaces (1870), and Lie groups, which use continuous or infinitesimal transformations.
		He used these groups to classify partial differential equations, making the traditional methods of solution all reduce to a single principle.
		Lie groups also provided a basis for the growth of modern topology.
	www.daviddarling.info /encyclopedia/L/Lie.html (151 words)

	AllRefer.com - Marius Sophus Lie (Mathematics, Biography) - Encyclopedia (Site not responding. Last check: 2007-11-06)
		AllRefer.com - Marius Sophus Lie (Mathematics, Biography) - Encyclopedia
		Marius Sophus Lie[mA´rEoos sO´foos lE] Pronunciation Key, 1842–99, Norwegian mathematician.
		More articles from AllRefer Reference on Marius Sophus Lie
	reference.allrefer.com /encyclopedia/L/Lie-Mari.html (139 words)

	Seminar Sophus Lie
		Seminar Sophus Lie is a joint Seminar of a group of German mathematicians interested in the theory of Lie groups and their wider horizon.
		It was founded around 1989-90 when, during the Volkskammer Government of the German Democratic Republic in 1989, open contacts between mathematicians in East- and Westgermany became a reality for the first time since 1961.
		Journal of Lie Theory is a journal for speedy publication of information in the following areas: Lie algebras, Lie groups, algebraic groups, and related types of topological groups such as locally compact and compact groups.
	www.math.tu-clausthal.de /~majhi/Seminare/SSLallg.html (331 words)

	MARIUS SOPHUS LIE - LoveToKnow Article on MARIUS SOPHUS LIE (Site not responding. Last check: 2007-11-06)
		Lie was a foreign member of the Royal Society, as well as an honorary member of the Cambridge Philosophical Society and the London Mathematical Society, and his geometrical inquiries gained him the muchcoveted honor of the Lobatchewsky prize.
		An analysis of Lies works is given in the Bibliotheca Mathematica (Leipzig, 1900).
		To properly cite this MARIUS SOPHUS LIE article in your work, copy the complete reference below:
	www.1911encyclopedia.org /L/LI/LIE_MARIUS_SOPHUS.htm (216 words)

	Lie group - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		If G and H are Lie groups (both real or both complex), then a Lie-group-homomorphism f : G
		The representation theory of simple Lie groups is the best and most important example.
		Sometimes, real Lie groups are defined as topological manifolds with continuous group operations; this definition is equivalent to our definition given above.
	www.xahlee.org /_p/wiki/Lie_group.html (1378 words)

	Great Norwegians -- Page 2
		Marius Sophus Lie -- Biography from the website of the University of St. Andrews in Scotland.
		Lie, Trygve Halvdan (Norway) -- Biography on homepage of the United Nations.
		Lie, Trygve Halvdan -- Brief entry in Columbia Electronic Encyclopedia.
	www.mnc.net /norway/Page2.htm (1090 words)

	Sophus Lie 2004/1
		In particular, subjects of interest are Lie algebras, Lie groups, Lie semigroups, homogeneous spaces and their geometry, applications of Lie theory to the theory of differential equations, symmetries...
		A class of Z_2-gaded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated.
		We treat the connected almost differentiable left A-loops as images of global differentiable sharply transitive sections $\sigma :G/H \to G$ for a Lie group $G$ with the properties $\sigma(H)=1 \in G$ and $\sigma (G/H)$ generates $G$ such that the subset $\sigma (G/H)$ is invariant under the conjugation with the elements of $H$.
	www.boku.ac.at /math/SSL2004/sl2004.html (1420 words)

	The Mathematics Genealogy Project - M. Sophus Lie
		Click here to see the students listed in chronological order.
		According to our current on-line database, M. Sophus Lie has 4 students and 511 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=18235 (108 words)

	Program LIE for Lie analysis of differential equations (Site not responding. Last check: 2007-11-06)
		Program LIE for Lie analysis of differential equations
		There is now a companion program BIGLIE51 that can handle problems that are too big for LIE.
		Look at the readme file from the program LIE.
	archives.math.utk.edu /software/msdos/adv.diff.equations/lie/.html (67 words)

	Alibris: Sophus Lie
		by Hermann, Robert, and Lie, Sophus, and Ackerman, M. see all copies from $2.95!
		by Hermann, Robert, and Lie, Sophus, and Ackerman, M. see all copies from $21.95!
		We guarantee the condition of every book, new or used.
	www.alibris.com /search/books/author/Sophus_Lie (105 words)

	Sophus Lie Conference Center (Site not responding. Last check: 2007-11-06)
		Sophus Lie Conference Center for mathematics was established through a collaboration between the mathematical departments at NTNU in Trondheim and University of Oslo and Eid kommune.
		During the summer this will be a meetingplace for students, teachers and researchers, with different kinds of workshops and conferences.
		Phone (+47) 22 85 59 17 / 22 85 58 87
	www.math.uio.no /nordfjordeid/nordfjord.html (180 words)

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