nLab David E. Radford

David E. Radford is an American algebraist, retired at the University of Illinois at Chicago.

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An example of finite dimensional noncommutative Hopf algebras is named after him (Radford’s Hopf algebras) with most famous member in dimension 8. The purpose of his example originally was to give an example of a Hopf algebra whose Jacobson radical is not a Hopf ideal.

Selected writings

Radford’s Hopf algebras were exhibited in

• D. E. Radford, On the coradical of a finite-dimensional Hopf algebra Proc. Am. Math. Soc. 53 (1975) 9–15.

On Yetter-Drinfeld modules over bialgebras:

• David E. Radford, Jacob Towber, Yetter–Drinfel’d categories associated to an arbitrary bialgebra, J. Pure Appl. Algebra 87 (1993), 259–279 MR94f:16060 doi

• R. G. Heyneman, David E. Radford, Reflexivity and coalgebras of finite type, J. Alg. 28 (1974) 215-246 pdf

On the quantum Yang-Baxter equation and quantum groups:

• Larry A. Lambe, David E. Radford: Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach, Mathematics and Its Applications 423, Springer, Kluwer (1997) [doi:10.1007/978-1-4615-4109-7]

On Hopf algebras:

• David E. Radford, Hopf algebras, Series on Knots and Everything: Volume 49, 588 pp. World Scientific 2011 doi

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