Publications of David E. Radford
On Automorphisms of Biproducts.
Comm. Alg.,
45(4):1365--1398, 2017.
Biproducts and Kashina's Examples.
Comm. Algebra,
44(1):174--204, 2016.
A Hopf Algebra Freeness Result Revisited.
Comm. Algebra,
43(4):1369--1376, 2015.
Hopf algebras, volume 49 of Series on Knots and Everything.
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. xxii+559 pp.
MR2894855
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
Complete reducibility theorems for modules over pointed Hopf algebras.
J. Algebra,
324(11):2932--2970, 2010.
MR2732981
Representations of pointed Hopf algebras and their Drinfel\cprime d quantum doubles.
J. Algebra,
321(9):2567--2603, 2009.
MR2504492
Pointed Hopf algebras---from enveloping algebras to quantum groups and beyond.
Acta Appl. Math.,
108(1):141--155, 2009.
MR2540963
On the simple representations of generalized quantum groups and quantum doubles.
J. Algebra,
319(9):3689--3731, 2008.
MR2407847
Biproducts and two-cocycle twists of Hopf algebras.
In Modules and comodules,
pages 331--355. Birkhäuser Verlag, Basel, 2008.
MR2742638
On the tensor product of an oriented quantum algebra with itself.
J. Knot Theory Ramifications,
16(7):929--957, 2007.
MR2354268
Hopf algebras and generalizations, volume 441 of Contemporary Mathematics.
American Mathematical Society, Providence, RI, 2007.
MR2385183
Trace-like functionals on the double of the Taft Hopf algebra.
J. Algebra,
301(1):1--34, 2006.
MR2230318
Finite-dimensional Hopf algebras of rank one in characteristic zero.
J. Algebra,
302(1):214--230, 2006.
MR2236601
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
Diagrammatic morphisms and applications, volume 318 of Contemporary Mathematics.
American Mathematical Society, Providence, RI, 2003.
MR1973455
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
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
On the even powers of the antipode of a finite-dimensional Hopf algebra.
J. Algebra,
251(1):185--212, 2002.
MR1900281
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
Oriented quantum algebras, categories and invariants of knots and links.
J. Knot Theory Ramifications,
10(7):1047--1084, 2001.
MR1867109
Oriented quantum algebras and invariants of knots and links.
J. Algebra,
246(1):253--291, 2001.
MR1872620
On a parameterized family of twist quantum coalgebras and the bracket polynomial.
J. Algebra,
225(1):93--123, 2000.
MR1743652
A separation result for quantum coalgebras with an application to pointed quantum coalgebras of small dimension.
J. Algebra,
225(1):162--200, 2000.
MR1743656
Quantum algebras, quantum coalgebras, invariants of $1\text{-}1$ tangles and knots.
Comm. Algebra,
28(11):5101--5156, 2000.
MR1785491
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
Finite-dimensional simple-pointed Hopf algebras.
J. Algebra,
211(2):686--710, 1999.
MR1666665
Quantum algebra structures on $n\times n$ matrices.
J. Algebra,
213(2):405--436, 1999.
MR1673463
Generalized double crossproducts associated with the quantized enveloping algebras.
Comm. Algebra,
26(1):241--291, 1998.
MR1600690
Centrality and the KRH invariant.
J. Knot Theory Ramifications,
7(5):571--624, 1998.
MR1637585
Solutions to the quantum Yang-Baxter equation having certain bialgebras as their reduced FRT construction.
Illinois J. Math.,
42(4):630--654, 1998.
MR1649881
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
Semisimple Hopf algebras.
J. Algebra,
171(1):5--35, 1995.
MR1314091
Invariants of $3$-manifolds derived from finite-dimensional Hopf algebras.
J. Knot Theory Ramifications,
4(1):131--162, 1995.
MR1321293
Solutions to the quantum Yang-Baxter equation arising from pointed bialgebras.
Trans. Amer. Math. Soc.,
343(1):455--477, 1994.
MR1201324
The trace function and Hopf algebras.
J. Algebra,
163(3):583--622, 1994.
MR1265853
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
Algebraic aspects of the quantum Yang-Baxter equation.
J. Algebra,
154(1):228--288, 1993.
MR1201922
On quantum Yang-Baxter operators derived from finite-dimensional Hopf algebras.
Comm. Algebra,
21(4):1141--1152, 1993.
MR1209924
Minimal quasitriangular Hopf algebras.
J. Algebra,
157(2):285--315, 1993.
MR1220770
Yetter-Drinfel\cprime d categories associated to an arbitrary bialgebra.
J. Pure Appl. Algebra,
87(3):259--279, 1993.
MR1228157
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
Solutions to the quantum Yang-Baxter equation and the Drinfel\cprime d double.
J. Algebra,
161(1):20--32, 1993.
MR1245841
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
On the antipode of a quasitriangular Hopf algebra.
J. Algebra,
151(1):1--11, 1992.
MR1182011
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
On the quasitriangular structures of a semisimple Hopf algebra.
J. Algebra,
141(2):354--358, 1991.
MR1125700
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
Semisimple cosemisimple Hopf algebras.
Amer. J. Math.,
110(1):187--195, 1988.
MR926744
Finite-dimensional cosemisimple Hopf algebras in characteristic $0$ are semisimple.
J. Algebra,
117(2):267--289, 1988.
MR957441
Divided power structures on Hopf algebras and embedding Lie algebras into special-derivation algebras.
J. Algebra,
98(1):143--170, 1986.
MR825139
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
The structure of Hopf algebras with a projection.
J. Algebra,
92(2):322--347, 1985.
MR778452
On the antipode of a cosemisimple Hopf algebra.
J. Algebra,
88(1):68--88, 1984.
MR741933
A Hopf module characterization of Hopf algebras.
Proc. Amer. Math. Soc.,
88(1):8--10, 1983.
MR691268
On the structure of pointed coalgebras.
J. Algebra,
77(1):1--14, 1982.
MR665161
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
The cofree irreducible Hopf algebra on a separable field extension.
J. Algebra,
70(2):527--547, 1981.
MR623824
On an analog of Lagrange's theorem for commutative Hopf algebras.
Proc. Amer. Math. Soc.,
79(2):164--166, 1980.
MR565330
On bialgebras which are simple Hopf modules.
Proc. Amer. Math. Soc.,
80(4):563--568, 1980.
MR587928
When pro-affine monoid schemes are group schemes.
J. Algebra,
57(2):497--501, 1979.
MR533810
Embedding commutative irreducible Hopf algebras into cofree irreducible Hopf algebras.
Comm. Algebra,
7(12):1211--1243, 1979.
MR538327
A natural ring basis for the shuffle algebra and an application to group schemes.
J. Algebra,
58(2):432--454, 1979.
MR540649
The cofree irreducible Hopf algebra on an algebra.
Amer. J. Math.,
101(5):1025--1045, 1979.
MR546301
On the structure of commutative pointed Hopf algebras.
J. Algebra,
50(2):284--296, 1978.
MR0463227
Operators on Hopf algebras.
Amer. J. Math.,
99(1):139--158, 1977.
MR0437581
Pointed Hopf algebras are free over Hopf subalgebras.
J. Algebra,
45(2):266--273, 1977.
MR0437582
Finiteness conditions for a Hopf algebra with a nonzero integral.
J. Algebra,
46(1):189--195, 1977.
MR0447314
Freeness (Projectivity) criteria for Hopf algebras over Hopf subalgebras.
J. Pure Appl. Algebra,
11(1-3):15--28, 1977/78.
MR0476790
The order of the antipode of a finite dimensional Hopf algebra is finite.
Amer. J. Math.,
98(2):333--355, 1976.
MR0407069
Commutative nearly primitively generated Hopf algebras.
Comm. Algebra,
4(9):823--872, 1976.
MR0427360
The antipode of a finite-dimensional Hopf algebra over a field has finite order.
Bull. Amer. Math. Soc.,
81(6):1103--1105, 1975.
MR0396650
Forms of certain Hopf algebras.
Manuscripta Math.,
17(4):333--338, 1975.
MR0396651
On a coradical of a finite-dimensional Hopf algebra.
Proc. Amer. Math. Soc.,
53(1):9--15, 1975.
MR0396652
Reflexivity and coalgebras of finite type.
J. Algebra,
28:215--246, 1974.
MR0346001
On the structure of ideals of the dual algebra of a coalgebra.
Trans. Amer. Math. Soc.,
198:123--137, 1974.
MR0346002
Coalgebraic coalgebras.
Proc. Amer. Math. Soc.,
45:11--18, 1974.
MR0357474
Coreflexive coalgebras.
J. Algebra,
26:512--535, 1973.
MR0327818
On the union of closed sets of a finite dimensional vector space.
Amer. Math. Monthly,
79:759--761, 1972.
MR0302662
On the convergence of the zeta function of a commutative ring.
Duke Math. J.,
38:521--526, 1971.
MR0279081
A free rank $4$ Hopf algebra with antipode of order $4$.
Proc. Amer. Math. Soc.,
30:55--58, 1971.
MR0279161