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Showing 1 to 20 of 22 for “"Hopf Algebras"”.
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Cocommutative Hopf algebras with antipode.
Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1965. Ph.D.
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Theta Maps for Combinatorial Hopf Algebras
… Sottile show that the peak algebra is the odd Hopf sub-algebra of quasi symmetric functions using their theory of combinatorial Hopf algebras. In all these cases, there is a very natural and well-behaved Hopf algebra morphism from quasi-symmetric functions or non-commutative symmetric functions …
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The Pointed-Irreducible Dualization of Hopf-Algebras
Made available in DSpace on 2014-12-11T18:23:56Z (GMT). No. of bitstreams: 1 7317207.pdf: 1994579 bytes, checksum: 0aec9cb41d8822750580cd85fe3e8713 (MD5) Previous issue date: 1972
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Inductive constructions for Lie bialgebras and Hopf algebras
… years, two generalisations of the theory of Lie algebras have become prominent, namely the "semi-classical" theory of Lie bialgebras and the "quantum" theory of Hopf algebras, including the quantized enveloping algebras. I develop an inductive approach to the study of these objects. An important …
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Relations in the homotopy of simplicial abelian Hopf algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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EXTENDING ACTIONS OF HOPF ALGEBRAS TO ACTIONS OF THE DRINFEL'D DOUBLE
… mathematical objects, e.g. some noncommutative algebras. It is generally agreed that the right generalizations of group actions to solve this problem are actions of Hopf algebras, the study of which has exploded in the years since the publication of Sweedler's Hopf algebras in 1969. Different …
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Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups
… which ensure that the bicrossproduct of two Hopf $\sp{\*}$ algebras is a Hopf $\sp{\*}$ algebra. In Appendix B, we provide physical motivation for studying bicrossproducts by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct.
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Actions of finite dimensional non-commutative, non-cocommutative Hopf algebras on rings
… the ring of invariants for some class of "nice" algebras under finite dimensional Hopf algebra actions. We begin with an introduction to the general study of Hopf algebras and their basic properties, then explain why they are a natural choice to generalize the action of finite groups on rings. We …
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Autonomous Pseudomonoids
… dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. Autonomous pseudomonoids were introduced in [13] as generalisations of both autonomous monoidal categories and Hopf algebras. Much of the theory of autonomous …
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An introduction to the theory of quantum groups
… This background material includes vector spaces, algebras and coalgebras, bialgebras, Hopf algebras, and Lie algebras. The understanding gained from these subjects is then used to explore some of the more basic, albeit important, quantum groups. The thesis ends with an indication of how to proceed …
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Q-OSCILLATORS AND THEIR APPLICATIONS
The recent focus on deformations of algebras called quantum algebras can be attributed to the fact that they appear to be the basic algebraic structures underlying an amazingly diverse set of physical situations. To date many interesting features of these algebras have been found and they are now …
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Computational methods for higher real K-theory with applications to tmf
We begin by present a new Hopf algebra which can be used to compute the tmf homology of a space or spectrum at the prime 3. Generalizing work of Mahowald and Davis, we use this Hopf algebra to compute the tmf homology of the classifying space of the symmetric group on three elements. We also …
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Bicharacter Construction of Quantum Vertex Algebras
… is a study of the axiomatics of quantum vertex algebras based on the bicharacter construction suggested by R. Borcherds in [Bor01]. One of the goals is to use the ideas of [Bor01] to incorporate the examples of quantum vertex operators in the literature ([Jin91], [Jin95], [FR92], [FR97]), in …
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Rigid Analytic Quantum Groups
… of $G$ respectively. We show that these algebras are topological Hopf algebras and, by adapting techniques extracted from work of Ardakov-Wadsley, Schmidt and Emerton in $p$-adic representation theory, we also show that they are Fréchet-Stein algebras and use this to investigate an …
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Analysis and Implementation of Algorithms for Noncommutative Algebra
… in mind. Different encodings of <I>associative algebras</I> and <I>modules</I> are also considered. To effectively analyze these algorithms and encodings, the <I>encoding neutral</I> analysis framework is introduced. This framework builds on the ideas used in the arithmetic complexity framework …
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Polynomial Identities on Algebras with Actions
… of this result which applies to associative algebras whose induced Lie or Jordan algebras are G-graded. Group-gradings and actions by a group of automorphisms are examples of Hopf algebras acting on H-algebras. If H is finite-dimensional, semisimple, commutative, and splits over its base …
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Multiparameter quantum groups: contractions and coloured generalisations.
… quantum groups and associated structure of Hopf algebras. We focus our attention on a new quantum group, Gr,s, depending on two deformation parameters and five generators. The first four generators of this Hopf algebra form a Hopf subalgebra which coincides exactly with the single-parameter …
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