# Hopf algebras: an introduction

All right, what about the book under review? My point is made: these are pretty austere and imposing beasts, and there is no fast-and-easy way to get at them. Here Hopf algebras play a dual role: first the left invariant differential operators on an algebraic group form a cocommutative Hopf algebra, which coincides with the enveloping algebra of the Lie algebra in characteristic 0, but not in characteristic p. Second: the regular functions on an affine algebraic group, under ordinary multiplication, form a commutative Hopf algebra.

So there is an awful lot going on! With this as the context for Hopf algebras, what about the book under review? This said, a caveat is in order. With the aforementioned definition occurring on p. Beyond this, the reader is certainly well-advised to hit the exercises in the book with zeal and commitment, even if he has a decent background in commutative algebra, algebraic geometry and category theory. In any case, once Hopf algebras have been properly introduced and the whole affair gets off the ground, the focus falls on Hopf orders cf.

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The Spectrum of a Ring. The Zariski Topology on the Spectrum. Representable Group Functors. Hopf Algebras. Larson Orders. Knots and Primes. Masanori Morishita.

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Abstract Algebra. Clive Reis. The Corona Problem. Eric T.

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## HOPF Algebras: An Introduction

Clifford Algebras and Lie Theory. Eckhard Meinrenken. Symbol Correspondences for Spin Systems. Pedro de M. Algebra 2. Ramji Lal. Geometric Aspects of General Topology. Katsuro Sakai. A Primer for Undergraduate Research. Aaron Wootton. Handbook of the Geometry of Banach Spaces. Analytic Aspects of Convexity. Gabriele Bianchi. Additive Number Theory. David Chudnovsky. Semigroups, Algebras and Operator Theory. P G Romeo. Classical and Multilinear Harmonic Analysis: Volume 1. Algebraic Theory of Locally Nilpotent Derivations.

Gene Freudenburg. Syzygies and Homotopy Theory. The Theory of Nilpotent Groups. Marcos Zyman.

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Groups, Matrices, and Vector Spaces. James B. Jonathan S. Function Theory on Planar Domains. Stephen D. Jim Cogdell. Lie Groups. Daniel Bump. Ralph E. Friedrich Wehrung.

Algebra 1. Problems from the Discrete to the Continuous. Ross G. Lie Groups: Structure, Actions, and Representations. Ivan Penkov. Probability Theory. Achim Klenke. Linear Discrete Parabolic Problems.

## Algebra 2 page 338

Nikolai Bakaev. Operator Algebra and Dynamics. Toke M. Catherine Donati-Martin. Fundamentals of Modern Algebra. Robert G Underwood. Computational Techniques for the Summation of Series. Anthony Sofo. Asymptotic Geometric Analysis. Monika Ludwig. Fundamentals of Hopf Algebras. Robert G. How to write a great review. The review must be at least 50 characters long.

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## HOPF Algebras: An Introduction - PDF Free Download

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