(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.

(50)
Gerstenhaber brackets on Hochschild cohomology of twisted tensor products
(with Lauren Grimley and Van C. Nguyen),
*J. Noncommutative Geometry* 11 (2017), no. 4, 1351-1379.

(51)
The Gerstenhaber bracket as a Schouten bracket for polynomial rings extended by finite groups
(with Cris Negron), *Proc. London Math. Soc.* (3) 115 (2017), no. 6,
1149-1169.

A longer version with an appendix containing some computational details is
here.

(52)
Tensor products and support varieties for some noncocommutative Hopf algebras
(with Julia Plavnik),
*Algebras and Representation Theory* 21 (2018), no. 2, 259-276.

(53)
PBW deformations of braided products
(with Chelsea Walton), *J. Algebra* 504 (2018), 536-567.

(54)
Deforming group actions on Koszul algebras
(with Anne Shepler), *Mathematical Research Letters*
25 (2018), no. 5, 1613-1644.

(55)
Varieties for modules of finite dimensional Hopf algebras,
* Geometric and Topological Aspects of the Representation
Theory of Finite Groups*,
Proceedings of the Pacific Institute for the Mathematics Sciences
Summer School and Workshop, July 27-August 5, 2016,
Springer 2018, 481-495.

(56)
Finite generation of some cohomology rings via twisted tensor product
and Anick resolutions (with Van C. Nguyen and Xingting Wang),
*J. Pure Appl Algebra* 223 (2019), no. 1, 316-339.

A longer version with details of calculations is
here.

(57)
Color Lie rings and PBW deformations of skew group algebras
(with S. Fryer, T. Kanstrup, E. Kirkman, and A.V. Shepler),
*Journal of Algebra* 518 (2019), 211-236.

(58)
Resolutions for twisted tensor products
(with Anne Shepler), *Pacific J. Math* 298 (2019), no. 2, 445-469.

(59)
*Hochschild Cohomology for Algebras*,
Graduate Studies in Mathematics 204, American Mathematical Society, 2019.

(60)
A_{∞}-coderivations and the Gerstenhaber bracket on Hochschild cohomology
(with C. Negron and Y. Volkov), *J. Noncommutative Geometry* 14 (2020), no. 2, 531-565.

(61)
Gerstenhaber brackets on Hochschild cohomology of general
twisted tensor products
(with T. Karadag, D. McPhate, P. Ocal, and T. Oke),
*J. Pure Appl. Algebra* 225 (2021), no. 6, 14 pp.

(62)
Support varieties for finite tensor categories:
Complexity, realization, and connectedness
(with P. A. Bergh and J. Y. Plavnik),
*J. Pure Appl. Algebra* 225 (2021), no. 9, 21 pp.

(63)
Group-twisted Alexander-Whitney and Eilenberg-Zilber maps
(A.V. Shepler), *Algebras and Representation Theory* 24 (2021), no. 2, 357-366.

Gerstenhaber brackets for skew group algebras
in positive characteristic
(A.V. Shepler), to appear in *Transformation Groups*.

Delta sets and polynomial identities in pointed Hopf algebras
(with Yuri Bahturin), to appear in *Algebras and Representation Theory*.

Homotopy liftings and Hochschild cohomology of some twisted tensor products
(with Tolulope Oke and Pablo Ocal), to appear in
*Journal of Algebra and Its Applications*.

Cohomology rings of finite-dimensional pointed Hopf algebras
over abelian groups
(with Nicolas Andruskiewitsch, Ivan Angiono, and Julia Pevtsova),
to appear in *Research in the Mathematical Sciences*.

New approaches to finite generation of cohomology rings
(with V. C. Nguyen and X. Wang), to appear in
*Journal of Algebra*.

Hochschild cohomology of twisted tensor products
(with Benjamin Briggs), to appear in
*Mathematische Zeitshrift.*

Lie brackets on Hopf algebra cohomology
(with Tekin Karadag), to appear in
*Pacific J. Math.*

Graded Lie structure on cohomology of some exact monoidal categories (with Yury Volkov), submitted.