Hopf Algebras

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Hopf Algebras

Heinz Hopf The tensor product; algebras, coalgebras, bialgebras, Hopf algebras. Bialgebras and Hopf algebras from the point of. We make here a small excursion into the setting of Hopf algebras, which are directly related to algebraic groups, but which will also be useful in the conceptual. for and extend by linearity to all of. For general Hopf algebras, the comultiplication is given in Sweedler notation. That is, if then Monoidal Functors, Species and Hopf Algebras Marcelo Aguiar Swapneel Mahajan Department of Mathematics Texas AM University College Station, TX. CHAPTER 1 Bialgebras and Hopf algebras We de ne bialgebras, Hopf Algebras, and related algebraic structures, largely following the original paper [? Hopf algebras occur naturally in algebraic topology, A subalgebra A of a Hopf algebra H is a Hopf subalgebra if it is a subcoalgebra of H and the antipode S maps. Introduction Hopf algebras are named after Heinz Hopf who discovered them the last century in the context of algebraic topology [Hopf 1941. Caution: convention in topology. In algebraic topology, it is common to define Hopf algebras without mentioning the antipode, since in many topological cases. Rent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone. Hopf Algebras Zajj Daugherty March 6, 2012 Big idea: The Hopf algebra structure is essentially what one needs in order to guarantee that tensor products of modules. Representation theory of Hopf algebras. In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field K is a Kvector space V with an action H V V usually denoted by juxtaposition ( that is, the image of (h, v) is written hv ). HOPF ALGEBRAS AND LIE ALGEBRAS UCHICAGO PROSEMINAR JANUARY 9, 2014 3 2. Let kbe a commutative ring with unit. We start by formulating a familiar denition in a possibly unfamiliar way: Denition. A primer of Hopf algebras Pierre Cartier Institut Mathematique de JussieuCNRS, 175 rue du Chevaleret, F Paris cartier@ihes. Alain Connes David Kazhdan Moss Sweedler HOPF ALGEBRAS IN COMBINATORICS DARIJ GRINBERG AND VICTOR REINER Contents Introduction 2 1. Coalgebras 5 JOURNAL OF PURE AND APPLIED ALGEBRA J5IsvIBa Journal of Pure and Applied Algebra 100 (1995) 7392 Hopf algebras and invariants of 3manifolds I have the following situation: Let, A, B be Hopf algebras, with B having actually the structure of an algebra in the category of Abimodules (this comes from. I have just seen the tensor algebra for a Lie algebra. Let \mathfrakg be a Lie algebra, and let T(\mathfrakg) be its tensor algebra. Correspondencia Galois de acoes de algebras de Hopf em algebras primas: Corpo base k de caracterstica zero (Portuguese Edition) This paper o ers an introduction to Hopf algebras. Rather, it is a paper providing the necessary structures in order to construct a Hopf algebra. It examines tensor products, algebras, coalgebras, bialgebras, and homology groups.

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