Dr. Ellen Kirkman

Professor of Mathematics

Dr. Kirkman’s

  • Office: Manchester 386
  • Phone: (336) 758-5351
  • Email: kirkman 'at' wfu.edu
PhD in Mathematics and M.S. in Statistics Michigan State University, 1975
Noncommutative Algebra, Representation Theory, and Homological Algebra
Computational invariant theory, computational algebraic geometry, and quantum calculus.

  • Inertial coeffcient rings and the idempotent lifting property, Proc. Amer. Math. Soc. 61 (1976), 217-222.
  •  The Pierce representation of an inertial coeffcient ring, Rocky Mountain J. Math. 8 (1978), 533-538.
  •  Orders over hereditary rings, J. Algebra 55 (1978), 1-27 (with James Kuz- manovich).
  •  Hereditary module finite algebras, J. London Math. Soc. (2) 19 (1979), 268-276 (with John Fuelberth and James Kuzmanovich).
  •  Hereditary finitely generated algebras satisfying a polynomial identity, Proc. Amer. Math. Soc. 83 (1981), 461-466 (with James Kuzmanovich).
  •  Hereditary rings integral over their centers, J. Algebra 102 (1986), 119-128 (with James Kuzmanovich).
  •  Right hereditary affne PI rings are left hereditary, Glasgow Math. J. 30 (1988), 115-120 (with James Kuzmanovich).
  •  Matrix subrings having finite global dimension, J. Algebra 109 (1987), 74-92 (with James Kuzmanovich).
  •  On the global dimension of a ring modulo its nilpotent radical, Proc. Amer. Math. Soc. 102 (1988), 25-28 (with James Kuzmanovich).
  •  On the global dimension of fibre products, Pacific J. Math. 134 (1988), 121-132 (with James Kuzmanovich)
  •  Global dimensions of a class of tiled orders, J. Algebra 127 (1989), 57-72 (with James Kuzmanovich).
  •  Finitistic dimension of finite dimensional monomial algebras, J. Algebra 136 (1991), 37-50 (with Edward Green and James Kuzmanovich).
  •  Algebras with large homological dimensions, Proc. Amer. Math. Soc. 109 (1990), 903-6 (with James Kuzmanovich).
  • Finitistic dimension in Noetherian rings, J. Algebra 147 (1992), 350-364 (with James Kuzmanovich and Lance Small).
  •  Q-analogs of harmonic oscillators and related rings, Israel J. Math. 81 (1993), 111-127 (with Lance Small).
  •  Constructing projective resolutions, Comm. Alg. 21 (1993), 1869-1887 (with Charles D. Feustel, Edward L. Green, and James Kuzmanovich).
  •  On the finitistic dimension of fixed subrings, Comm. Algebra 22 (10) (1994), 3755-5774 (with James Kuzmanovich).
  •  A q-analog of the Virasora algebra, Comm. Algebra 22 (1994), 3755-3774 (with Claudio Procesi and Lance Small).
  •  Minimal prime ideals in enveloping algebras of Lie superalgebras, Proc. Amer. Math. Soc. 124 (1996), no. 6, 16931702 (with James Kuzmanovich)
  •  Global and Krull dimensions of quantum Weyl algebras, J. Algebra. 216 (1999) 405-416 (with Hisaaki Fujita and James Kuzmanovich).
  •  Noetherian down-up algebras, Proc. Amer. Math. Soc. 127 (1999), 3161-3167 (with Ian Musson and Donald Passman).
  •  The primitivity of Noetherian down-up algebras, Comm. Algebra 28 (2000), no. 6, 2983{2997 (with James Kuzmanovich).
  •  Non-Noetherian down-up algebras, Comm. Algebra 28 (2000), no. 11, 5255{ 5268 (with James Kuzmanovich).
  •  Examples of FCR algebras, Comm. Algebra 30 (2002)(7), 3311{3326 (with Lance Small).
  •  Hopf down-up algebras, J. Algebra 262 (2003), 42-53 (with Ian Musson).
  •  Fixed subrings of Noetherian graded regular rings, Journal of Algebra 288 (2005) no. 2, 463{484 (with James Kuzmanovich).
  •  Down-up algebras from trees, Comm. Algebra 34 (2006), no. 10, 3785{3799 (with James Kuzmanovich).
  •  Rigidity of graded regular algebras, Trans. Amer. Math. Soc. 360 (2008), 6331-6369 (with James Kuzmanovich and James Zhang).
  • Gorenstein subrings of invariants under Hopf algebra actions, J. Algebra. 322(2009) no. 10, 3640{3669 (with James Kuzmanovich and James Zhang).
  •  Shephard-Todd-Chevalley theorem for skew polynomial rings, Algebr. Repre- sent. Theory 13 (2010) no. 2, 127{158 (with James Kuzmanovich and James Zhang).
  •  Finiteness conditions on the Yoneda algebra of a monomial algebra, J. Pure Appl. Algebra 218 (2014), no. 1, 52{64 (with Andrew Conner, James Kuz- manovich, and W Frank Moore).
  •  Invariants of (-1)-skew polynomial rings under permutation representations. Recent advances in representation theory, quantum groups, algebraic geome- try, and related topics, 155{192, Contemp. Math., 623, Amer. Math. Soc., Providence, RI, 2014 (with James Kuzmanovich and James Zhang).
  •  Invariant theory of finite group actions on down-up algebras, Transformation Groups 20 (2015) no. 1, 113-165 (with James Kuzmanovich and James Zhang).
  •  Periodic free resolutions from twisted matrix factorizations, J. Algebra 455 (2016), 137{163 (with Thomas Cassidy, Andrew Conner, and W. Frank Moore).
  •  Quantum binary polyhedral groups and their actions on quantum planes, J. Reine Angew. Math. 719 (2016), 211{252 (with Kenneth Chan, Chelsea Walton, James Zhang).
  •  Noncommutative complete intersections, J. Algebra 429 (2015), 253{286 (with James Kuzmanovich and James Zhang).
  •  The invariant thoery of Artin-Schelter regular algebras: A survey, Recent Devel- opments in Representation Theory (Maurice Auslander Distinguished Lectures and International Conference, May 1-6, 2014, Woods Hole Oceanographic In- stitute, Woods Hole, MA), Contemp. Math. 673, p. 25-50, Amer. Math. Soc., Providence, RI., 2016.
  •  On the discriminant of twisted tensor products, J. Algebra 477 (2017), 29-55 (with Jason Gaddis and W. Frank Moore).
  •  Nakayama automorphism and rigidity of dual re ection group coactions, J. Al- gebra 487 (2017), 60-92. (with James Kuzmanovich and James Zhang).
  • Rigidity of down-up algebras with respect to finite group coactions, J. Pure and Applied Algebra 221 (2017) No. 12 3089-3103 (with Jianmin Chen and James Zhang).
  •  McKay correspondence for semisimple Hopf actions on regular graded algebras I, J. Algebra 508 (2018), 512{538 (with Kenneth Chan, Chelsea Walton, James Zhang).
  •  McKay correspondence for semisimple Hopf actions on regular graded algebras II, J. Noncommut. Geom. 13 (2019), no. 1, 87{114. (with Kenneth Chan, Chelsea Walton, James Zhang).
  •  Auslander's Theorem for permutation actions on noncommutative algebras, Proc. Amer. Math. Soc. 147 (2019), no. 5, 1881{1896. (with Jason Gaddis, W. Frank Moore, and Robert Won).
  •  Color Lie algebras and PBW deformations of skew group algebras, J. Algebra 518 (2019), 211{236. (with S. Fryer, T. Kanstrup, A.V. Shepler, and W. With- erspoon).
  •  Auslander's Theorem for group coactions on Noetherian down-up algebras Trans- form. Groups 25 (2020) No. 4, 1037{1062, (with J. Chen and James Zhang). 46. Noncommutative Knorrer periodicity and noncommutative Kleinian singulari- ties. J. Algebra 540 (2019), 234{273. (with Andrew Conner, W. Frank Moore, and Chelsea Walton).
  •  Three infinite families of re ection Hopf algebras, J. Pure Appl. Algebra, 224 (2020), no. 8, 106315, 34 (with Luigi Ferraro, W. Frank Moore, and Robert Won).
  •  Semisimple re ection Hopf algebras of dimension sixteen (with Luigi Ferraro, W. Frank Moore, and Robert Won), submitted, arXiv 1907.06763.
  •  The Jacobian, re ection arrangement and discriminant for re ection Hopf al- gebras (with James Zhang), to appear Int. Math. Res. Not., arXiv 1902.00421.
  •  On the Noether bound for noncommutative rings (with Luigi Ferraro, W. Frank Moore and Kewen Peng), to appear in Proc. Amer. Math. Soc., arXiv 1907.06761.
  • McKay Matrices for Finite-dimensional Hopf Algebras (with Georgia Benkart, Rekha Biswall, Van Nguyen, and Jieru Zhu), submitted, arXiv 2007.05510.
  •  Degree bounds for Hopf actions on Artin-Schelter regular algebras (with Robert Won and James Zhang), submitted, arXiv 2008.05047.
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