Results 41 to 50 of about 133 (132)
Mathematische Zeitschrift, 1992 Lannes' \(T\) functor is the left adjoint to the functor \(M\mapsto H^*(B({\mathbb{Z}}/p{\mathbb{Z}}))\oplus M\) in the category of unstable modules over the Steenrod algebra. If \(A\) is a Hopf algebra over the Steenrod algebra as well as an unstable module then \(T(A)\) is a Hopf algebra. In this paper we derive a general form for \(T(A)\) when \(A\)
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Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes [PDF]
Journal of High Energy Physics, 2012 We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values.
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Hopf algebras, from basics to applications to renormalization
, 2004 Minor corrections, BCH approach precised in subsection II.6, references added.
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From left modules to algebras over an operad: application to combinatorial Hopf algebras
Annales mathématiques Blaise Pascal, 2010 The purpose of this paper is two fold: we study the behaviour of the forgetful functor from 𝕊 -modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras.
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Simulating the Hadamard gate in the Fibonacci disk code for universal topological quantum computation. [PDF]
Innovation (Camb), 2023 Wu YS.
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A central closure construction for certain algebra extensions. Applications to Hopf actions
Journal of Pure and Applied Algebra, 2005 Let \(k\) be a commutative ring with unit, \(A\) be a \(k\)-algebra and consider the `multiplication algebra' of \(A\), i.e. the \(R\)-subalgebra \(M(A):=\langle L_a,R_a\mid a\in A\rangle\subseteq\text{End}_k(A)\), where \(L_a\) (resp. \(R_a)\) is the left (resp. right) multiplication with \(a\).
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STRUCTURE OF CORADICAL FILTRATION AND ITS APPLICATION TO HOPF ALGEBRAS OF DIMENSIONpq [PDF]
Glasgow Mathematical Journal, 2008 AbstractThis paper contributes to the classification problem ofpqdimensional Hopf algebrasHover an algebraically closed fieldkof characteristic 0, wherep,qare odd primes. It is shown that such Hopf algebrasHare semisimple for the pairs of odd primes (p,q)=(3,11),(3,13),(3,19),(5,17),(5,19),(5,23),(5,29),(7,17),(7,19),(7,23),(7,29),(11,29),(13,29).
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Braided Hopf algebras, double constructions, and applications
, 2015 This thesis contains four related papers which study different aspects of double constructions for braided Hopf algebras. The main result is a categorical action of a braided version of the Drinfeld center on a Heisenberg analogue, called the Hopf center.
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Induced Representations of Hopf Algebras: Applications to Quantum Groups at Roots of 1
Journal of Algebra, 1993 The author establishes a connection between the induction functors and the associated cohomology theories of the quantum enveloping algebra of a semisimple Lie algebra of type \(A_{n-1}\) and the quantum linear group defined by \textit{B. Parshall} and \textit{J. Wang} [Quantum linear groups (Mem. Am. Math. Soc. 439) (1991; Zbl 0724.17011)].
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