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Showing 1 to 15 of 15 for “"Hopf Algebra"”.
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On Hopf Algebra Type and Rational Calculus Decompositions
… result to a much larger class of functors. A Hopf algebra A is both an algebra with a multiplication map m:A⊗A→ A and a coalgebra with a comultiplication map D: A→A⊗A which must behave well with respect to each other. Mimicking this definition, we say that an object X …
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A Hopf Algebra Generalization of the Wever-Specht Formula
Made available in DSpace on 2014-12-11T18:23:37Z (GMT). No. of bitstreams: 1 7114758.pdf: 936818 bytes, checksum: dcbbb62bb327654aa3686034cbedeb7c (MD5) Previous issue date: 1970
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Coend elements of a Hopf algebra in a braided rigid monoidal category
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01
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Theta Maps for Combinatorial Hopf Algebras
… thesis introduces a way to generalize of peak algebra. There are several equivalent denitions for the peak algebra. Stembridge describes it via enriched P-partitions to generalize marked shifted tableaux and Schur's Q functions. Nyman shows that it is a the sum of permutations with the same …
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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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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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Stable characters for symmetric groups and wreath products
Given a Hopf algebra R, the Grothendieck group of C = R-mod inherits the structure of a ring. We define a ring [mathematical equation]), which is "the [mathematical equation] limit" of the Grothendieck rings of modules for the wreath products [mathematical equation]; it is the Grothendieck group of …
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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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Studies on quasisymmetric functions
… one of the standard examples of a combinatorial Hopf algebra. In this thesis, I elucidate three aspects of its theory: 1) Gessel's P-partition enumerators are quasisymmetric functions that generalize, and share many properties of, the Schur functions; their Hopf-algebraic antipode satisfies a …
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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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Algebraic structures in stochastic differential equations
… the inverse of the original mapping. The shuffle Hopf algebra and its associated convolution algebra play important roles in the their analysis, arising from the combinatorial structure of iterated Stratonovich integrals. It was recently shown that the algebra generated by iterated It^o integrals …
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Quantized multiplicative quiver varieties and actions of higher genus braid groups
In this thesis, a new class of algebras called quantized multiplicative quiver varieties A (Q), is constructed, depending upon a quiver Q, its dimension vector d, and a certain "moment map" parameter . The algebras Ad(Q) are obtained via quantum Hamiltonian reduction of another algebra D,(Matd(Q)) …
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Multiparameter quantum groups: contractions and coloured generalisations.
This thesis is devoted to various algebraic as well as differential geometric aspects of multi- parameter quantum groups. In particular, we study some two-parameter quantum groups and associated structure of Hopf algebras. We focus our attention on a new quantum group, Gr,s, depending on two …
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Physics on Noncommutative Spacetimes
… of the spacetime through a noncommutative algebra of functions defined on it. We call such spacetimes 'noncommutative spacetimes'. This dissertation probes physics on several such spacetimes. These include compact noncommutative spaces called fuzzy spaces and noncompact spacetimes. The …
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Quantum Yang-Baxter Equation: Algebraic Constructions and Categorical Perspectives
L'abstract è presente nell'allegato / the abstract is in the attachment