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Topic: Pseudogroup

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	Pseudogroup - Wikipedia, the free encyclopedia
		The further requirement on a pseudogroup is related to the possibility of patching (in the sense of descent, transition functions, or a gluing axiom).
		An example in space of two dimensions is the pseudogroup of invertible holomorphic functions of a complex variable (invertible in the sense of having an inverse function).
		The concept of a local Lie group, namely a pseudogroup of functions defined in neighbourhoods of the origin of E, is actually closer to Lie's original concept of Lie group, in the case where the transformations involved depend on a finite number of parameters, than the contemporary definition via manifolds.
	en.wikipedia.org /wiki/Pseudogroup (490 words)

	Abstract For Colloquium of January 16,1998 (Site not responding. Last check: 2007-10-31)
		A pseudogroup of local diffeomorphisms of an analytic manifold is said to be a Lie pseudogroup if it is the set of solutions of an involutive exterior differential system.
		Cartan showed that any Lie pseudogroup can be characterized geometrically as the set of local automorphisms of a reduction of the frame bundle of a manifold associated to the given differential system.
		The Lie pseudogroups defined by exterior differential systems which are completely integrable in the sense of the Frobenius theorem are said to be of finite type, since their elements are parametrized locally by arbitrary constants.
	www.math.ubc.ca /Dept/Events/colloquia/kamran.html (292 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Pseudogroups over {1..n} for n=5: 1 2 3 4 5 2 1 4 5 3 3 5 1 2 4 4 3 5 1 2 5 4 2 3 1 and it's transposed.
		Since the number of latin squares grows very fast, this additional factor is not very important for big n.
		n=15 this calculation gives about 10^88 reduced latin squares and 10^83 pseudogroups over {1,2,..,15}.
	www.math.niu.edu /~rusin/known-math/99/pseudogroup (149 words)

	Research - Shiing Shen Chern (Site not responding. Last check: 2007-10-31)
		He was a true follower of Élie Cartan, working intensely on the theory of equivalence in his time in China from 1937-1943, in relative isolation.
		In 1954 he published his own treatment of the pseudogroup problem that is in effect the touchstone of Cartans geometric theory.
		He used the moving frame method with success only matched by its inventor, he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory.
	mywebpage.netscape.com /Afra2837/shiing-shen-chern-research.html (125 words)

	Infinite Lie pseudogroups (Site not responding. Last check: 2007-10-31)
		Although he was optimistic Lie was unable to extend his infinitesimal structure theory to an infinitesimal structure theory of infinite parameter Lie pseudogroups.
		This standard form is used to predict a model of the pseudogroup defining system.
		In summary we obtained an effective algorithm which from the infinitesimal determining system can determine whether a pseudogroup of symmetries is isomorphic to a transitive pseudogroup.
	www.cecm.sfu.ca /~reid/DetResDesMat/DetResDes/node12.html (288 words)

	UNIDO
		It would not be a good idea to generate a group for each author, containing the author and his delegees and explicitly give them permissions on the documents of this author.
		Instead pseudogroups are implemented, being so called as they are no real groups, but basically function as such.
		As the author is an element of the metadata and may be changed at any time, we generate the pseudogroup at run-time.
	www.unido.org /doc/doc/user-group-permission (450 words)

	Moving Frames for Pseudo-Groups. II. Differential Invariants for Submanifolds (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		Abstract: This paper is the second in a series that develops a theory of moving frames for pseudogroup actions.
		In this paper, we define a moving frame for free pseudo-group action on the submanifolds, illustrated by explicit examples.
		3 Geometry and structure of Lie pseudogroups from infinitesima..
	citeseer.ist.psu.edu /627507.html (644 words)

	Citebase - Invariants of pseudogroup actions: Homological methods and Finiteness theorem (Site not responding. Last check: 2007-10-31)
		We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action.
		The corresponding differential invariants are determined via formal theory and lead to the notions of k-variants and k-covariants, even in the case of non-integrable pseudogroup.
		Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology and prove the finiteness theorem.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0511711 (157 words)

	Finite parameter Lie groups of symmetries of PDEs
		The key idea of the algorithm was to calculate in the space of initial data of the system; rather than the generally incalculable space of solutions of the system.
		As a generalization of Lie groups to the infinite case, such infinite pseudogroups are subject to severe practical and theoretical difficulties.
		the pseudogroup of local conformal transformations and the pseudogroup of local volume preserving diffeomorphisms).
	www.cecm.sfu.ca /~reid/DetResDesMat/DetResDes/node11.html (488 words)

	Geometry and structure of Lie pseudogroups from infinitesimal defining systems - Lisle, Reid (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		Abstract: In this paper we give a method which uses a finite number of differentiations and linear operations to determine the Cartan structure of structurally transitive Lie pseudogroups from their infinitesimal defining equations.
		These equations are the linearized form of the pseudogroup defining system -- the system of pdes whose solutions are the transformations belonging to the pseudogroup.
		In many applications the explicit form of the transformations is not available and we only have access to...
	citeseer.ist.psu.edu /lisle94geometry.html (885 words)

	A very incomplete list of papers on groupoids
		Written in Russian, this paper apparently did not come to the attention of most semigroup theorists until its translation appeared in 1979.
		Uesugi, T., A note on the topological groupoid associated with a pseudogroup of transformations, Bull.
		Uesugi, T., On the relations between the groupoid and the pseudogroup of transformations, Bull.
	www.cameron.edu /~koty/groupoids/1961.htm (789 words)

	XI. INVARIANCE GROUP of G(n)
		Passage to the ray or projective space, normalizing the Hilbert vectors, allowing them to be interpreted in the usual way as probability distributions.
		In the Heisenberg picture, CCR as an expression in the observables is left form invariant under the transformations of dynamical evolution.
		In either picture, the algebraic form of CCR is left invariant under transformations of the full unitary pseudogroup.
	graham.main.nc.us /~bhammel/FCCR/XI.html (2441 words)

	Request Tracker Documentation
		These users can not be granted rights or responsibilites (except as members of pseudogroups (see below)).
		To allow any user to create a ticket in any queue, grant the right 'CreateTicket' to the Pseudogroup 'Everyone' globally.
		To allow any user to create a ticket in the queue 'general', grant the right 'CreateTicket' to the pseudogroup 'Everyone' for the queue 'general'
	www.helgrim.com /rtdocs/admin.html</FONT (821 words)

	Manfred Du Schuh - Pseudogruppe ; Pseudogroup - SCHUH, JOHAN (Site not responding. Last check: 2007-10-31)
		Manfred Du Schuh - Pseudogruppe ; Pseudogroup - SCHUH, JOHAN
		SCHUH, JOHAN Manfred Du Schuh - Pseudogruppe ; Pseudogroup
		They offer full satisfaction and normal prices - no markups, no hidden costs, no overcharged shipping costs.
	www.antiqbook.com /boox/buc/152054.shtml (75 words)

	A very incomplete list of papers on groupoids
		Gray, J.W., A theory of pseudogroups with applications to contact structures, Technical Report No. 65 Applied Mathematics and Statistics Laboratory Stanford University, California, 1957.
		This report describes the relationship between a topological groupoid and a pseudogroup.
		Haefliger, A., Structures feuilletees et cohomologie a valeur dans un faisceau de groupoids, Comment.
	www.cameron.edu /~koty/groupoids/1900.htm (428 words)

	58Hxx (Site not responding. Last check: 2007-10-31)
		58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
		58H05 Pseudogroups and differentiable groupoids, See also {22A22, 22E65}
		58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.), See also {57R32}
	www-math.cudenver.edu /~mbrezina/MR/58Hxx.html (49 words)

	Wolak: Foliated and associated geometric structures on foliated manifolds
		).- Pseudogroups of local isometries, Differential Geometry, L.A.Cordero ed., Proceedings Vth International Colloquium on Differential Geometry, Santiago de Compostela 1984,
		- Le problème d'équivalence pour les pseudogroupes de Lie, méthodes intrinsèques, Bull.
		A.M. The first and second fundamental theorems of Lie for Lie pseudogroups, Amer.
	www.numdam.org /numdam-bin/item?id=AFST_1989_5_10_3_337_0 (303 words)

	ON QUANTUM THEORETICAL ORIGINS OF NEWTONIAN TIME
		Here is a brief reminder of the general importance of the invariance of the uncertainty relations of QM derived from CCR.
		The unitary pseudogroup also contains that Galilean group.
		This is to say that the unitary pseudo group contains all the mathematical equipment necessary to implement transformations of frame that are: translations, rotations and "boosts", with related inner and outer actions on the algebra.
	graham.main.nc.us /~bhammel/PHYS/newtqtime.html (15355 words)

	Find in a Library: Deformation theory of pseudogroup structures,
		Find in a Library: Deformation theory of pseudogroup structures,
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		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	www.worldcatlibraries.org /wcpa/ow/481a2b170bc6410e.html (44 words)

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