Publications of David E. Radford

David E. Radford.  On Automorphisms of Biproducts.  Comm. Alg., 45(4):1365--1398, 2017.
David E. Radford.  Biproducts and Kashina's Examples.  Comm. Algebra, 44(1):174--204, 2016.
David E. Radford.  A Hopf Algebra Freeness Result Revisited.  Comm. Algebra, 43(4):1369--1376, 2015.
David E. Radford.  Hopf algebras, volume 49 of Series on Knots and Everything.  World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. xxii+559 pp.  MR2894855
Louis Kauffman and David E. Radford.  Oriented quantum algebras and coalgebras, invariants of oriented $1$--$1$ tangles, knots and links.  In Cross disciplinary advances in quantum computing, pages 95--132.  Amer. Math. Soc., Providence, RI, 2011. MR2768795
Nicolás Andruskiewitsch, David Radford and Hans-Jürgen Schneider.  Complete reducibility theorems for modules over pointed Hopf algebras.  J. Algebra, 324(11):2932--2970, 2010. MR2732981
Leonid Krop and David E. Radford.  Representations of pointed Hopf algebras and their Drinfel\cprime d quantum doubles.  J. Algebra, 321(9):2567--2603, 2009. MR2504492
David E. Radford.  Pointed Hopf algebras---from enveloping algebras to quantum groups and beyond.  Acta Appl. Math., 108(1):141--155, 2009. MR2540963
David E. Radford and Hans-Jürgen Schneider.  On the simple representations of generalized quantum groups and quantum doubles.  J. Algebra, 319(9):3689--3731, 2008. MR2407847
David E. Radford and Hans Jürgen Schneider.  Biproducts and two-cocycle twists of Hopf algebras.  In Modules and comodules, pages 331--355.  Birkhäuser Verlag, Basel, 2008. MR2742638
David E. Radford.  On the tensor product of an oriented quantum algebra with itself.  J. Knot Theory Ramifications, 16(7):929--957, 2007. MR2354268
Louis H. Kauffman, David E. Radford and Fernando J. O. Souza, editors.  Hopf algebras and generalizations, volume 441 of Contemporary Mathematics.  American Mathematical Society, Providence, RI, 2007. MR2385183
David E. Radford and Sara Westreich.  Trace-like functionals on the double of the Taft Hopf algebra.  J. Algebra, 301(1):1--34, 2006. MR2230318
Leonid Krop and David E. Radford.  Finite-dimensional Hopf algebras of rank one in characteristic zero.  J. Algebra, 302(1):214--230, 2006. MR2236601
Leonid Krop and David E. Radford.  Simple modules for the Drinfel\cprime d double of a class of Hopf algebras.  In Groups, rings and algebras, pages 229--235.  Amer. Math. Soc., Providence, RI, 2006. MR2279242
David E. Radford, Fernando J. O. Souza and David N. Yetter, editors.  Diagrammatic morphisms and applications, volume 318 of Contemporary Mathematics.  American Mathematical Society, Providence, RI, 2003. MR1973455
Louis H. Kauffman and David Radford.  Bi-oriented quantum algebras, and a generalized Alexander polynomial for virtual links.  In Diagrammatic morphisms and applications (San Francisco, CA, 2000), pages 113--140.  Amer. Math. Soc., Providence, RI, 2003. MR1973514
David E. Radford.  On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra.  J. Algebra, 270(2):670--695, 2003. MR2019635
David E. Radford and Hans-Jürgen Schneider.  On the even powers of the antipode of a finite-dimensional Hopf algebra.  J. Algebra, 251(1):185--212, 2002. MR1900281
David E. Radford.  On quantum algebras and coalgebras, oriented quantum algebras and coalgebras, invariants of $1$-$1$ tangles, knots and links.  In New directions in Hopf algebras, pages 263--319.  Cambridge Univ. Press, Cambridge, 2002. MR1913441
Louis Kauffman and David E. Radford.  Oriented quantum algebras, categories and invariants of knots and links.  J. Knot Theory Ramifications, 10(7):1047--1084, 2001. MR1867109
Louis H. Kauffman and David E. Radford.  Oriented quantum algebras and invariants of knots and links.  J. Algebra, 246(1):253--291, 2001. MR1872620
David E. Radford.  On a parameterized family of twist quantum coalgebras and the bracket polynomial.  J. Algebra, 225(1):93--123, 2000. MR1743652
Louis Kauffman and David E. Radford.  A separation result for quantum coalgebras with an application to pointed quantum coalgebras of small dimension.  J. Algebra, 225(1):162--200, 2000. MR1743656
Louis Kauffman and David E. Radford.  Quantum algebras, quantum coalgebras, invariants of $1\text{-}1$ tangles and knots.  Comm. Algebra, 28(11):5101--5156, 2000. MR1785491
Louis H. Kauffman and David E. Radford.  On two proofs for the existence and uniqueness of integrals for finite-dimensional Hopf algebras.  In New trends in Hopf algebra theory (La Falda, 1999), pages 177--194.  Amer. Math. Soc., Providence, RI, 2000. MR1800712
David E. Radford.  Finite-dimensional simple-pointed Hopf algebras.  J. Algebra, 211(2):686--710, 1999. MR1666665
Louis H. Kauffman and David E. Radford.  Quantum algebra structures on $n\times n$ matrices.  J. Algebra, 213(2):405--436, 1999. MR1673463
David E. Radford.  Generalized double crossproducts associated with the quantized enveloping algebras.  Comm. Algebra, 26(1):241--291, 1998. MR1600690
Louis H. Kauffman, David Radford and Stephen Sawin.  Centrality and the KRH invariant.  J. Knot Theory Ramifications, 7(5):571--624, 1998. MR1637585
Larry Lambe and David E. Radford.  Solutions to the quantum Yang-Baxter equation having certain bialgebras as their reduced FRT construction.  Illinois J. Math., 42(4):630--654, 1998. MR1649881
Larry A. Lambe and David E. Radford.  Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach, volume 423 of Mathematics and its Applications.  Kluwer Academic Publishers, Dordrecht, 1997. MR1483071
Richard G. Larson and David E. Radford.  Semisimple Hopf algebras.  J. Algebra, 171(1):5--35, 1995. MR1314091
Louis H. Kauffman and David E. Radford.  Invariants of $3$-manifolds derived from finite-dimensional Hopf algebras.  J. Knot Theory Ramifications, 4(1):131--162, 1995. MR1321293
David E. Radford.  Solutions to the quantum Yang-Baxter equation arising from pointed bialgebras.  Trans. Amer. Math. Soc., 343(1):455--477, 1994. MR1201324
David E. Radford.  The trace function and Hopf algebras.  J. Algebra, 163(3):583--622, 1994. MR1265853
David E. Radford.  On Kauffman's knot invariants arising from finite-dimensional Hopf algebras.  In Advances in Hopf algebras (Chicago, IL, 1992), pages 205--266.  Dekker, New York, 1994. MR1289427
Larry A. Lambe and David E. Radford.  Algebraic aspects of the quantum Yang-Baxter equation.  J. Algebra, 154(1):228--288, 1993. MR1201922
David E. Radford.  On quantum Yang-Baxter operators derived from finite-dimensional Hopf algebras.  Comm. Algebra, 21(4):1141--1152, 1993. MR1209924
David E. Radford.  Minimal quasitriangular Hopf algebras.  J. Algebra, 157(2):285--315, 1993. MR1220770
David E. Radford and Jacob Towber.  Yetter-Drinfel\cprime d categories associated to an arbitrary bialgebra.  J. Pure Appl. Algebra, 87(3):259--279, 1993. MR1228157
Louis H. Kauffman and David E. Radford.  A necessary and sufficient condition for a finite-dimensional Drinfel\cprime d double to be a ribbon Hopf algebra.  J. Algebra, 159(1):98--114, 1993. MR1231205
David E. Radford.  Solutions to the quantum Yang-Baxter equation and the Drinfel\cprime d double.  J. Algebra, 161(1):20--32, 1993. MR1245841
David E. Radford.  Irreducible representations of ${\mathcal U}_ q(g)$ arising from ${\rm Mod}^ \bullet_ {C^ {1/2}}$.  In Quantum deformations of algebras and their representations (Ramat-Gan, 1991/1992; Rehovot, 1991/1992), pages 143--170.  Bar-Ilan Univ., Ramat Gan, 1993. MR1261906
David E. Radford.  On the antipode of a quasitriangular Hopf algebra.  J. Algebra, 151(1):1--11, 1992. MR1182011
Robert Grossman and David Radford.  A simple construction of bialgebra deformations.  In Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), pages 115--117.  Amer. Math. Soc., Providence, RI, 1992. MR1187281
David E. Radford.  On the quasitriangular structures of a semisimple Hopf algebra.  J. Algebra, 141(2):354--358, 1991. MR1125700
David E. Radford.  The group of automorphisms of a semisimple Hopf algebra over a field of characteristic $0$ is finite.  Amer. J. Math., 112(2):331--357, 1990. MR1047302
Richard G. Larson and David E. Radford.  Semisimple cosemisimple Hopf algebras.  Amer. J. Math., 110(1):187--195, 1988. MR926744
Richard G. Larson and David E. Radford.  Finite-dimensional cosemisimple Hopf algebras in characteristic $0$ are semisimple.  J. Algebra, 117(2):267--289, 1988. MR957441
David E. Radford.  Divided power structures on Hopf algebras and embedding Lie algebras into special-derivation algebras.  J. Algebra, 98(1):143--170, 1986. MR825139
Kenneth Newman and David E. Radford.  On when a separable field extension in characteristic $p>0$ is determined by its Frobenius structure. II.  J. Algebra, 102(2):301--331, 1986. MR853246
David E. Radford.  The structure of Hopf algebras with a projection.  J. Algebra, 92(2):322--347, 1985. MR778452
David E. Radford.  On the antipode of a cosemisimple Hopf algebra.  J. Algebra, 88(1):68--88, 1984. MR741933
David E. Radford.  A Hopf module characterization of Hopf algebras.  Proc. Amer. Math. Soc., 88(1):8--10, 1983. MR691268
David E. Radford.  On the structure of pointed coalgebras.  J. Algebra, 77(1):1--14, 1982. MR665161
David E. Radford.  On when a separable field extension in characteristic $p>0$ is determined by its Frobenius structure. I.  J. Algebra, 79(1):127--150, 1982. MR679975
David E. Radford.  The cofree irreducible Hopf algebra on a separable field extension.  J. Algebra, 70(2):527--547, 1981. MR623824
David E. Radford.  On an analog of Lagrange's theorem for commutative Hopf algebras.  Proc. Amer. Math. Soc., 79(2):164--166, 1980. MR565330
David E. Radford.  On bialgebras which are simple Hopf modules.  Proc. Amer. Math. Soc., 80(4):563--568, 1980. MR587928
David E. Radford.  When pro-affine monoid schemes are group schemes.  J. Algebra, 57(2):497--501, 1979. MR533810
David E. Radford.  Embedding commutative irreducible Hopf algebras into cofree irreducible Hopf algebras.  Comm. Algebra, 7(12):1211--1243, 1979. MR538327
David E. Radford.  A natural ring basis for the shuffle algebra and an application to group schemes.  J. Algebra, 58(2):432--454, 1979. MR540649
Kenneth Newman and David E. Radford.  The cofree irreducible Hopf algebra on an algebra.  Amer. J. Math., 101(5):1025--1045, 1979. MR546301
David E. Radford.  On the structure of commutative pointed Hopf algebras.  J. Algebra, 50(2):284--296, 1978. MR0463227
David E. Radford.  Operators on Hopf algebras.  Amer. J. Math., 99(1):139--158, 1977. MR0437581
David E. Radford.  Pointed Hopf algebras are free over Hopf subalgebras.  J. Algebra, 45(2):266--273, 1977. MR0437582
David E. Radford.  Finiteness conditions for a Hopf algebra with a nonzero integral.  J. Algebra, 46(1):189--195, 1977. MR0447314
David E. Radford.  Freeness (Projectivity) criteria for Hopf algebras over Hopf subalgebras.  J. Pure Appl. Algebra, 11(1-3):15--28, 1977/78. MR0476790
David E. Radford.  The order of the antipode of a finite dimensional Hopf algebra is finite.  Amer. J. Math., 98(2):333--355, 1976. MR0407069
David E. Radford.  Commutative nearly primitively generated Hopf algebras.  Comm. Algebra, 4(9):823--872, 1976. MR0427360
David E. Radford.  The antipode of a finite-dimensional Hopf algebra over a field has finite order.  Bull. Amer. Math. Soc., 81(6):1103--1105, 1975. MR0396650
David E. Radford, Earl J. Taft and Robert Lee Wilson.  Forms of certain Hopf algebras.  Manuscripta Math., 17(4):333--338, 1975. MR0396651
David E. Radford.  On a coradical of a finite-dimensional Hopf algebra.  Proc. Amer. Math. Soc., 53(1):9--15, 1975. MR0396652
Robert G. Heyneman and David E. Radford.  Reflexivity and coalgebras of finite type.  J. Algebra, 28:215--246, 1974. MR0346001
David E. Radford.  On the structure of ideals of the dual algebra of a coalgebra.  Trans. Amer. Math. Soc., 198:123--137, 1974. MR0346002
D. E. Radford.  Coalgebraic coalgebras.  Proc. Amer. Math. Soc., 45:11--18, 1974. MR0357474
David E. Radford.  Coreflexive coalgebras.  J. Algebra, 26:512--535, 1973. MR0327818
D. E. Radford.  On the union of closed sets of a finite dimensional vector space.  Amer. Math. Monthly, 79:759--761, 1972. MR0302662
David E. Radford.  On the convergence of the zeta function of a commutative ring.  Duke Math. J., 38:521--526, 1971. MR0279081
David E. Radford.  A free rank $4$ Hopf algebra with antipode of order $4$.  Proc. Amer. Math. Soc., 30:55--58, 1971. MR0279161
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