Sarah Witherspoon

Publications

(1) The ring of equivariant vector bundles on finite sets, J. Algebra 175 (1995), 274-286.

(2) The representation ring of the quantum double of a finite group, J. Algebra 179 (1996), 305-329.
Based on my PhD thesis, which includes more details.

(3) The representation ring of the twisted quantum double of a finite group, Canad. J. Math. 48 (1996), 1324-1338.

(4) Irreducible representations of crossed products (with Susan Montgomery), J. Pure Appl. Algebra 129 (1998), 315-326.

(5) The Hochschild cohomology ring of a group algebra (with Stephen F. Siegel), Proc. London Math. Soc. 79 (1999), 131-157.

(6) The representation ring and the centre of a Hopf algebra, Canad. J. Math. 51 (1999), 881-896.

(7) Clifford correspondence for finite-dimensional Hopf algebras, J. Algebra 218 (1999), 608-620.

(8) A module-theoretic approach to Clifford theory for blocks, Proc. Amer. Math. Soc. 128 (2000), 661-670.

(9) The Hochschild cohomology ring of a cyclic block (with Stephen F. Siegel), Proc. Amer. Math. Soc. 128 (2000), 1263-1268.

(10) A Hopf structure for down-up algebras (with Georgia Benkart), Math. Z. 238 (2001), 523-553.

(11) Clifford correspondence for algebras, J. Algebra 256 (2002), 518-530.

(12) Hochschild cohomology and Linckelmann cohomology for blocks of finite groups (with Jonathan Pakianathan), J. Pure Appl. Algebra 178 (2003), 87-100.

(13) Algebraic deformations arising from orbifolds with discrete torsion (with A. Caldararu and A. Giaquinto), J. Pure Appl. Algebra 187 (2004), no. 1-3, 51-70.

(14) Representations of two-parameter quantum groups and Schur-Weyl duality (with G. Benkart), Hopf algebras, 65-92, Lecture Notes in Pure and Appl. Math., 237, Dekker, New York, 2004.

(15) Restricted two-parameter quantum groups (with G. Benkart), Representations of finite dimensional algebras and related topics in Lie theory and geometry, 293-318, Fields Inst. Commun. 40 , Amer. Math. Soc., Providence, RI, 2004.

(16) Products in Hochschild cohomology and Grothendieck rings of group crossed products, Adv. Math. 185 (2004), no. 1, 136-158.

(17) Two-parameter quantum groups and Drinfel'd doubles (with G. Benkart), Algebras and Representation Theory 7 (2004), 261-286.

(18) Quillen stratification for Hochschild cohomology of blocks (with J. Pakianathan and an appendix by S. F. Siegel), Trans. Amer. Math. Soc. 358 (2006), no. 7, 2897-2916.

(19) Skew derivations and deformations of a family of group crossed products, Comm. Algebra 34 (2006), no. 11, 4187-4206.

(20) Quantum group actions, twisting elements, and deformations of algebras (with G. Benkart), J. Pure Appl. Algebra 208 (2007), 371-389.

(21) Twisted graded Hecke algebras, J. Algebra 317 (2007), 30-42.

(22) Hochschild cohomology of smash products and rank one Hopf algebras (with Sebastian Burciu), Biblioteca de la Revista Matematica Iberoamericana Actas del "XVI Coloquio Latinoamericano de Algebra," (Colonia, Uruguay, 2005) , 2007, 153-170.

(23) Braid group representations from twisted quantum doubles of finite groups (with P. Etingof and E. Rowell), Pacific J. Math. 234 (2008), no. 1, 33-41.

(24) Hochschild cohomology and graded Hecke algebras (with Anne V. Shepler), Trans. Amer. Math. Soc. 360 (2008), no. 8, 3975-4005.

(25) Bialgebra cohomology, pointed Hopf algebras, and deformations (with Mitja Mastnak), J. Pure Appl. Algebra 213 (2009), 1399-1417.

(26) Hopf quivers and Nichols algebras in positive characteristic (with Claude Cibils and Aaron Lauve), Proc. Amer. Math. Soc. 137 (2009), no. 12, 4029-4041.

(27) Fusion subcategories of representation categories of twisted quantum doubles of finite groups (with Deepak Naidu and Dmitri Nikshych), Int. Math. Res. Not. (2009), no. 22, 4183-4219.

(28) Varieties for modules of quantum elementary abelian groups (with Julia Pevtsova), Algebras and Rep. Th. 12 (2009), no. 6, 567-595.

(29) Cohomology of finite dimensional pointed Hopf algebras (with Mitja Mastnak, Julia Pevtsova, and Peter Schauenburg), Proc. Lond. Math. Soc. (3) 100 (2010), no. 2, 377-404.

(30) Support varieties and representation type of small quantum groups (with Joerg Feldvoss), Int. Math. Res. Not. (2010), no. 7, 1346-1362. Erratum, Int. Math. Res. Not. (2015), no. 1, 288-290.

(31) Yetter-Drinfeld modules under cocycle twists (with Georgia Benkart and Mariana Pereira), J. Algebra 324 (2010), no. 11, 2990-3006.

(32) Hochschild cohomology of group extensions of quantum symmetric algebras (with Deepak Naidu and Piyush Shroff), Proc. Amer. Math. Soc. 139 (2011), 1553-1567.

(33) Finite groups acting linearly: Hochschild cohomology and the cup product (with Anne V. Shepler), Adv. Math. 226 (2011), no. 4, 2884-2910.

(34) Quantum differentiation and chain maps of bimodule complexes (with Anne V. Shepler), Algebra and Number Theory 5-3 (2011), 339-360.

(35) Support varieties and representation type of self-injective algebras (with Joerg Feldvoss), Homology, Homotopy and Applications 13 (2011), no. 2, 197-215.

(36) Group actions on algebras and the graded Lie structure of Hochschild cohomology (with Anne V. Shepler), J. Algebra 351 (2012), 350-381.

(37) Drinfeld orbifold algebras (with Anne V. Shepler), Pacific J. Math. 259-1 (2012), 161-193.

(38) Examples of support varieties for Hopf algebras with noncommutative tensor products (with Dave Benson), Archiv der Mathematik 102 (2014), no. 6, 513-520.

(39) A Poincare-Birkhoff-Witt Theorem for quadratic algebras with group actions (with Anne V. Shepler), Trans. Amer. Math. Soc. 366 (2014), no. 12, 6483-6506.

(40) Finite generation of the cohomology of some skew group algebras (with Van C. Nguyen), Algebra and Number Theory 8 (2014), no. 7, 1647-1657. (The version here includes some corrections to a proof in Section 5 that are also written up separately in this erratum.

(41) Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras (with Chelsea Walton), Algebra and Number Theory 8 (2014), no. 7, 1701-1731.

(42) PBW deformations of skew group algebras in positive characteristic (with Anne V. Shepler), Algebras and Representation Theory 18 (2015), no. 1, 257-280.

(43) Tensor ideals and varieties for modules of quantum elementary abelian groups (with Julia Pevtsova), Proceedings of the American Mathematical Society 143 (2015), no. 9, 3727-3741.

(44) Poincare-Birkhoff-Witt Theorems (with Anne Shepler), in Mathematical Sciences Research Institute Proceedings Commutative Algebra and Noncommutative Algebraic Geometry, Vol. 1, ed. D. Eisenbud, S.B. Iyengar, A.K. Singh, J.T. Stafford, and M. Van den Bergh, Cambridge Univ. Press, 2015.

(45) An alternate approach to the Lie bracket on Hochschild cohomology (with Cris Negron), Homology, Homotopy and Applications 18 (1) (2016), 265-285.

(46) PBW deformations of quantum symmetric algebras and their group extensions (with Piyush Shroff), J. Algebra and Its Applications 15 (2016), no. 3, 15 pp.

(47) Hopf automorphisms and twisted extensions (with Susan Montgomery and Maria D. Vega), J. Algebra and Its Applications 15 (2016), no. 6, 14 pp.

(48) Gerstenhaber brackets on Hochschild cohomology of quantum symmetric algebras and their group extensions (with Guodong Zhou), Pacific J. Math 283 (2016), no. 1, 223-255.

(49) Hochschild cohomology and quantum Drinfeld Hecke algebras (with Deepak Naidu), Selecta Mathematica 22 (2016), no. 3, 1537-1561.



Preprints

(1) Gerstenhaber brackets on Hochschild cohomology of twisted tensor products (with Lauren Grimley and Van C. Nguyen), to appear in J. Noncommutative Geometry.

(2) Tensor products and support varieties for some noncocommutative Hopf algebras (with Julia Plavnik), to appear in Algebras and Representation Theory.

(3) The Gerstenhaber bracket as a Schouten bracket for polynomial rings extended by finite groups (with Cris Negron), to appear in Proc. London Math. Soc.
A longer version with an appendix containing some computational details is here.

(4) PBW deformations of braided products (with Chelsea Walton), submitted.

(5) Deforming group actions on Koszul algebras (with Anne Shepler), submitted.

(6) Resolutions for twisted tensor products (with Anne Shepler), submitted.

(7) Varieties for modules of finite dimensional Hopf algebras, submitted.

(8) Finite generation of some cohomology rings via twisted tensor product and Anick resolutions (with Van C. Nguyen and Xingting Wang), submitted.
A longer version with details of calculations is here.

Notes

Cohomology of Hopf algebras

Book

An Introduction to Hochschild Cohomology (draft)