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Topic: Cocommutative

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	Formal group - Wikipedia, the free encyclopedia
		The formal group ring of a formal group law is a cocommutative Hopf algebra analogous to the group ring of a group and to the universal enveloping algebra of a Lie algebra, both of which are also cocommutative Hopf algebras.
		Its formal group ring (also called its hyperalgebra or its covariant bialgebra) is a cocommutative Hopf algebra H constructed as follows.
		For any cocommutative Hopf algebra, an element g is called group-like if Δg=g⊗g and ηg=1, and the group-like elements form a group under multiplication.
	en.wikipedia.org /wiki/Lazard_ring (2008 words)

	PlanetMath: almost cocommutative bialgebra
		is called almost cocommutative if there is an unit
		The significance of the almost cocommutative condition is that
		This is version 2 of almost cocommutative bialgebra, born on 2003-03-24, modified 2003-03-24.
	planetmath.org /encyclopedia/AlmostCocommutativeBialgebra.html (121 words)

	Yetter-Drinfel'd-Hopfalgebren
		In many cases, it is then possible to prove that this commutative and cocommutative Yetter-Drinfel'd Hopf algebra must be trivial, which leads to the conclusion that the initial Hopf algebra was a group ring or a dual group ring.
		that are nontrivial, commutative, cocommutative, semisimple, and cosemisimple.
		The part of Clifford theory used in the proof of the main results is a theorem of W. Chin that sets up a correspondence between orbits of the centrally primitive idempotents of the Yetter-Drinfel'd Hopf algebra and orbits of the simple modules of the Radford biproduct under the action of the one-dimensional characters.
	www.mathematik.uni-muenchen.de /~sommerh/Publikationen/YetterPrimwww/Yetterwww.html (1921 words)

	TOPOLOGISEMINAR (Site not responding. Last check: 2007-11-03)
		`Hochschild and cyclic cohomology of cocommutative Hopf algebras'
		Moreover, if $X$ is a member of the large and interesting class of spaces for which there exists a cocommutative Hopf algebra $(A,d)$ with homology isomorphic to that of $\Omega X$, then the Hochschild cohomology of $(A,d)$ is isomorphic as an algebra to the cohomology of the free loop space on $X$.
		It seems highly probable that the cyclic cohomology of $(A,d)$ is isomorphic as an algebra to the cohomology of the $S^1$-homotopy orbit space of the free loop space on $X$, though this remains work in progress.
	www.math.uio.no /~rognes/topsem/oppslag.090500.html (212 words)

	AMCA: The topos of ``cocommutative coalgebras'' by Robert Pare (Site not responding. Last check: 2007-11-03)
		AMCA: The topos of ``cocommutative coalgebras'' by Robert Pare
		The category of cocommutative coalgebras is almost a topos.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/j/f/24.htm (133 words)

	Springer Online Reference Works
		Essentially, all cocommutative Hopf algebras are group algebras.
		Here is an example of a Hopf algebra which is neither commutative nor cocommutative.
		Technically it is more convenient to deform not commutative Hopf algebras but cocommutative ones and to start not with a Poisson–Hopf algebra (or a Poisson–Lie group [a1], which is more or less the same) but with its infinitesimal version, called a Lie bi-algebra.
	eom.springer.de /q/q076310.htm (838 words)

	Modules of Solvable Infinitesimal Groups and the Structure of Representation-Finite Cocommutative Hopf Algebras - ... (Site not responding. Last check: 2007-11-03)
		In this paper we extend the representation and block theory of solvable infinitesimal groups to determine the structure of those cocommutative Hopf algebras over k that have finite representation type.
		Introduction In continuation of earlier work [7], we study in this paper the structure of cocommutative Hopf algebras of finite representation type.
		Modules of Solvable Infinitesimal Groups and the Structure of Representation-Finite Cocommutative Hopf Algebras.
	citeseer.ist.psu.edu /62249.html (664 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Cohomology and prjectivity of modules for finite group schemes Christopher P. Bendel Let G be a finite group scheme over a field k, that is, an affine group scheme whose coordinate ring k[G] is finite dimensional.
		Indeed, there is an equivalence of categories between finite group schemes and finite dimensional cocommutative Hopf algebras.
		Also, the mod-p Steenrod algebra is graded cocommutative so that some finite dimensional Hopf subalgebras are such algebras.
	www.maths.abdn.ac.uk /~bensondj/papers/b/bendel/cohproj.data (496 words)

	April 21-25 VU Math Events
		One of the basic examples of bicharacters are the commutation factors on abelian groups used, in particular, to define so called color Lie superalgebras, a notion generated in physics few decades ago.
		In general, bicharacters on a commutative and cocommutative Hopf algebra H allow one to define Lie structures on the algebras with the coaction H. On the other hand, Hopf algebras whose structure includes a fixed skew-symmetric bicharacter form an important class of cotriangular Hopf algebras, dual to the triangular ones introduced by Drinfeld.
		The goal of this talk is to report on most recent result in this area, including the extension of Scheunert's trick to arbitrary cocommutative Hopf algebras of characteristic different from 2 and the classification of finite-dimensional algebras, which are commutative under a suitable generalized Lie bracket.
	www.math.vanderbilt.edu /~calendar/archive/2003/04_21.html (449 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		While it is not specified, I take coalgebras to be coassociative, but not necessarily cocommutative.
		None of the remarks below apply to the cocommutative case.
		Let us assume that the model category structure would be the one "inherited" from dg modules; that is, a morphism of dg coalgebras would be a cofibration or weak equivalence if and only if it is as dg modules.
	www.lehigh.edu /~dmd1/pg214 (356 words)

	Citebase - Representation rings of quantum groups
		Authors: Domokos, M. Lenagan, T. Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental.
		This is a ring theoretic formulation of the well known fact that the representation theory of the quantized group is completely analogous to its classical counterpart.
		The subalgebras of cocommutative elements in the corresponding FRT-bialgebras (defined by Faddeev, Reshetikhin, and Takhtadzhyan) are explicitly determined, using a bialgebra embedding of the FRT-bialgebra into the tensor product of the quantized coordinate ring and the one-variable polynomial ring.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0308289 (639 words)

	Wednesday at the Streetfest III \| The String Coffee Table
		is a cocommutative bialgebra over a field of characteristic zero (say the complex numbers, if you’re a physicist).
		This generalizes a result of Milnor and Hopf, who showed that connected cocommutative bialgebras that are also COMMUTATIVE must be symmetric algebras.
		You start with the universal enveloping algebra of some Lie algebra L and you conclude that as a coalgebra it’s the same as the symmetric algebra of L, with its usual shuffle coproduct.
	golem.ph.utexas.edu /string/archives/000599.html (749 words)

	Amazon.ca: Brauer Groups, Hopf Algebras and Galois Theory: Books (Site not responding. Last check: 2007-11-03)
		Included is a systematic development of the theory of Grothendieck topologies and étale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit.
		Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra.
		The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear.
	www.amazon.ca /exec/obidos/ASIN/1402003463 (388 words)

	A Simpler Characterization of Sheffer Polynomials
		All these solutions can then be interpreted as cocommutative coalgebras.
		3 are interpreted as cocommutative coalgebras, and classified according to their coalgebraic properties.
		9 serve as the comultiplication of a (stronly) cohomogeneous cocommutative Hopf algebra over the symmetric functions, and conversely.
	pear.math.pitt.edu /mathzilla/Examples/sheffer.xml (1558 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		The principal investigator will determine suitable criteria for the ring of integers in a number field to be locally free over its Galois group ring.
		He will also work on the classification of commutative, cocommutative prime-power rank Hopf algebras.
		Number theory, which is the study of the properties of the whole numbers, is one of the oldest branches of mathematics.
	www.cs.utexas.edu /users/yguan/NSFAbstracts/Abstracts/MPS/DMS.MPS.a9001722.txt (114 words)

	Babytop - Fall 2003 (Site not responding. Last check: 2007-11-03)
		The short answer is because the diagonal map d : X -> X x X is cocommutative up to homotopy.
		That is, if T is the map from X x X to itself that switches the factors then Td is homotopic to d.
		(The more observant among you will notice that in fact Td = d so that d is strictly cocommutative.
	www-math.mit.edu /topology/babytop/abstracts/Mikeching.html (124 words)

	articulos
		Brauer group for cocommutative coalgebras (con Zhang Y., y F. Van Oystaeyen) J. Algebra 177 (1995), 536-568.
		Subgroups of the Brauer Group of a Cocommutative Coalgebra\cos (con J. Cuadra y J.R. Garc\'ia Rozas), J. Algebras and
		On the Brauer Group of a Cocommutative Irreducible Coalgebra (con J.
	www.ual.es /~btorreci/articulos.html (1063 words)

	Citations: Modules of Solvable Infinitesimal Groups and the Structure of Representation-Finite Cocommutative Hopf ...
		Citations: Modules of Solvable Infinitesimal Groups and the Structure of Representation-Finite Cocommutative Hopf Algebras - Farnsteiner, Voigt (ResearchIndex)
		Schemes of Tori and the Structure of Tame Restricted Lie..
		In the first section we show that the rank variety of an indecomposable module is an invariant of its stable Auslander Reiten component.
	citeseer.ist.psu.edu /context/542107/62249 (404 words)

	Citebase - Les algebres de Hopf des arbres enracines decores
		In citeKreimer1,Connes,Broadhurst,Kreimer2, a commutative, non cocommutative Hopf algebra H
		Its dual Hopf algebra is the enveloping algebra of the Lie algebra of rooted trees L
		In this paper, we introduce a non commutative, non cocommutative Hopf algebra H
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0105212 (1285 words)

	linear topology, hopf algebras and -autonomous categories (Site not responding. Last check: 2007-11-03)*
		We then extend Barr's work to vector spaces with additional structure, in particular to representations of Hopf algebras.
		As special cases, we examine cocommutative Hopf algebras, and quasitriangular Hopf algebras, also known as quantum groups.
		In the quasitriangular case, the representations actually form a braided *-autonomous category, first defined by the author.
	www.cis.upenn.edu /~bcpierce/types/archives/1993/msg00076.html (372 words)

	IngentaConnect Cocommutative Hopf Algebras of Permutations and Trees (Site not responding. Last check: 2007-11-03)
		IngentaConnect Cocommutative Hopf Algebras of Permutations and Trees
		Consider the coradical filtrations of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer.
		We give explicit isomorphisms showing that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980's by Grossman and Larson.
	www.ingentaconnect.com /content/klu/jaco/2005/00000022/00000004/00004628 (166 words)

	Dror Bar-Natan: Classes: 2003-04: Math 1350F - Knot Theory
		Class notes for Tuesday October 14, 2003 (computer study of A, some simple weight systems and the weight system of the Jones polynomial)
		Class notes for Thursday October 16, 2003 (A is associative commutative, coalgebras, A is coassociative and cocommutative)
		Class notes for Tuesday October 21, 2003 (coalgebras and duals of algebras, Hopf algebras, A is Hopf, Milnor-Moore and primitives, some primitives of A, trivalent vertices, the product of FT invariants is FT)
	www.math.toronto.edu /~drorbn/classes/0304/KnotTheory (538 words)

	Quantum Groups (Site not responding. Last check: 2007-11-03)
		The aim of this course is to understand the concept of quantum groups as constructed by V. Drinfeld (the background).
		Essentially quantum groups can be thought of as quantization of universal enveloping algebra of a Lie algebra, which has a structure of Hopf algebra (not cocommutative in general).
		In order to understand the concept of quantization better, we have to learn some mechanics (classical and quantum)
	www.math.neu.edu /~gautam_s/Spring06/QG/qg.html (204 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Formulae for the Eilenberg-Zilber theorem in this category have been given by Andy Tonks (thesis, available from Bangor math web site (/research/theses), and JPAA).
		So if \Pi K is the fundamental crossed complex of a simplicial set K, there is a diagonal map AW: \Pi K \to \Pi K \otimes \Pi K. This of course is not cocommutative, but there is, by acyclic models, a crossed complex homotopy h: T \circ AW \simeq AW.
		Can this process be pursued further as in Steenrod's original approach?
	www.lehigh.edu /~dmd1/rb927.txt (280 words)

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