My research focuses on quantum algebra, Hopf algebras, quantum groups, tensor categories, Poisson algebra, and noncommutative algebra. I am interested in how algebraic structures interact with representation theory, homological methods, categorical structures, and mathematical physics.

Looking forward, I am also interested in using computational and AI-assisted tools to explore examples, organize mathematical literature, test conjectures, and support rigorous mathematical research. My goal is to use these tools as assistants for mathematical exploration and exposition, while keeping proof, structure, and conceptual understanding at the center.

Research Interests

Selected Themes

Hopf algebras and quantum groups
Tensor categories and representation theory
Poisson and noncommutative algebra
Homological and computational methods

Hopf algebras and quantum groups

Quantum-symmetric equivalence is a graded Morita invariant, (with H. Huang, V. Nguyen, K. Vashaw and P. Veerapen), Proc. Amer. Math. Soc., 153 (2025), no. 4, 1389--1409.

On Hopf algebras of dimension $p^n$ in characteristic $p$, (with S.-H. Ng), Contemp. Math., 814 (2025), 151--181.

Twisting Manin's universal quantum groups and comodule algebras, (with H. Huang, V. Nguyen, C. Ure, K. Vashaw and P. Veerapen), Adv. Math., 445 (2024), Paper No. 109651, 55pp.

A cogroupoid associated to preregular forms, (with H. Huang, V. Nguyen, C. Ure, K. Vashaw and P. Veerapen), J. Noncommut. Geom., 18 (2024), no. 4, 1453--1483.

Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equations, (with H. Huang, V. Nguyen, C. Ure, K. Vashaw and P. Veerapen), Tranform. Groups, 29 (2024), no. 4, 1459--1500.

Gelfand-Kirillov dimension of cosemisimple Hopf algebras, (with A. Chirvasitu and C. Walton), Proc. Amer. Math. Soc., 147 (2019), 4665--4672.

Primitive deformations of quantum $p$-groups, (with V. Nguyen and L. Wang), Algebr. Represent. Theory 22 (2019), no.4, 837--865.

Hopf algebras of prime dimension in positive characteristic, (with S.-H. Ng), Bull. Lond. Math. Soc. 51 (2019), no. 3, 459--465.

A note on Masuoka's theorem for semisimple irreducible Hopf algebras, Arch. Math. (Basel) 113 (2019), no. 1, 11--20.

On quantum groups associated to a pair of preregular forms, (with A. Chirvasitu and C. Walton), J. Noncommut. Geom. 13 (2019), no. 1, 115--159.

On the structure and cohomology ring of connected Hopf algebras, (with K. Erdmann and O. Solberg), J. Algebra 527 (2019), 366--398.

Indicators of pointed Hopf algebras of dimension $pq$ over characteristic $p$, (with S.~Chen, T.~Liu, and L.~Wang), Missouri J. Math. Sci. 30 (2018), no. 2, 176--184.

Indicators of Hopf algebras in positive characteristic, (with L. Wang), Arch. Math. (Basel) 111 (2018), no. 5, 485--491.

A note on the bijectivity of antipode of a Hopf algebra and its applications, (with J.-F. Lu, S.-Q. Oh, and X.-L. Yu), Proc. Amer. Math. Soc. 146 (2018), no. 11, 4619--4631.

Pointed $p^3$-dimensional Hopf algebras in positive characteristic, (with V. Nguyen), Algebra Colloq. 25, no. 3 (2018), pp. 399--436.

Computing indicators of Radford algebras, (with H. Hu, X. Hu, and L. Wang), Involve, a journal of mathematics 11 (2018), no. 2, 325--334.

Calabi-Yau property under monoidal Morita-Takeuchi equivalence, (with X.-L. Yu and Y. Zhang), Pacific J. Math. 290 (2017), no. 2, 481--510.

On quantum groups associated to non-noetherian regular algebras of dimension 2, (with C. Walton), Math. Z. 284 (2016), no. 1, 543--574.

Isomorphism classes of finite-dimensional connected Hopf algebras in positive characteristic, Adv. Math. 281 (2015), 594--623.

Universal enveloping algebras of Poisson Hopf algebras, (with J.-F. Lu and G. Zhuang), J. Algebra 426 (2015), 92--136.

Classification of connected Hopf algebras of dimension $p^3$ I, (with V. Nguyen and L. Wang), J. Algebra 424 (2015), 473--505.

Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed field, (with L. Wang), Algebr. Represent. Theory 17 (2014), no. 4, 1267--1276.

Local criteria for cocommutative Hopf algebras, Comm. Algebra 42 (2014), no. 12, 5180--5191.

Connected Hopf algebras of dimension $p^2$, J. Algebra 391 (2013), 93--113.

Poisson algebras and noncommutative geometry

Weighted Poisson polynomial rings in dimension three, (with H. Huang, X. Tang, and J. J. Zhang), to appear J. Noncommut. Geom..

Poisson valuations, (with H. Huang, X. Tang, and J. J. Zhang), J. ~Algebra, 683 (2025), 1--59.

Twists of graded Poisson algebras and applications, (with X. Tang and J. J. Zhang), J. Geom. Phys., 207 (2025), No. 105344, 31pp.

A survey on Zariski cancellation problems for noncommutative and Poisson algebras, (with H. Huang and X. Tang), Contemp. Math., 801 (2024), no. 4, 1453--1483.

Reflection groups and rigidity of quadratic Poisson algebras, (with J. Gaddis and P. Veerapen), Algebr. Represent. Theory 26 (2023), 329--358.

Cancellation and skew cancellation for Poisson algebras, (with J. Gaddis and D. Yee), Math. Z. 301 (2022), 3503--3523.

Poisson geometry and representations of PI 4-dimensional Sklyanin algebras, (with C. Walton and M. Yakimov), Selecta Math. 27, (2021), 1--60.

Poisson Dixmier-Moeglin equivalence from a topological point of view, (with J. Luo and Q.-S. Wu), Israel J. Math., (2020), 1--37.

A note on the duality between Poisson homology and cohomology, (with J.-F. Lu and G. Zhuang), Comm. Algebra 48 (10) (2020), 4170-4175.

A note on generic Clifford algebras of binary cubic forms, (with L. Wang), Algebr. Represent. Theory 23 (4) (2020), 1797--1806.

The Zariski cancellation problem for Poisson algebras, (with J. Gaddis), J. Lond. Math. Soc. 101 (2020) no. 3, 1250--1279.

Nonsplit module extensions over the one-sided inverse of $k[x]$, (with Z.-P. Lu and L.~Wang), Involve, a journal of mathematics 12 (2019), no. 8, 1369--1377.

PBW-basis for universal enveloping algebras of differential graded Poisson algebras, (with X.-G. Hu and J.-F. Lu), Bull. Malays. Math. Sci. Soc. 42 (2019), no. 6, 3343--3377.

The Dixmier-Moeglin equivalence, Morita equivalence, and homeomorphism of spectra, (with J. Bell and D. Yee), J. Algebra 534 (2019), 228--244.

On $q$-commutative power and Laurent series rings at roots of unity, (with E. S. Letzter and L. Wang), Comm. Algebra 47 (2019), no. 5, 2149--2156.

Poisson geometry of PI three-dimensional Sklyanin algebras, (with C. Walton and M. Yakimov), Proc. Lond. Math. Soc. (3) 118 (2019), no. 6, 1471--1500.

Enveloping algebras of double Poison-Ore extensions, (with J.-F. Lu, S.-Q. Oh, and X.-L. Yu), Comm. Algebra 46 (2018), no. 11, 4891--4904.

The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras, (with M. Guo, X. Hu, and J.-F. Lu), Comm. Algebra 46, no. 6 (2018), pp. 2714--2729.

Homological unimodularity and Calabi-Yau condition for Poisson algebras, (with J.-F. Lu and G. Zhuang), Lett. Math. Phys. 107 (2017), no. 9, 1715--1740.

Universal enveloping algebras of Poisson-Ore extensions, (with J.-F. Lu and G. Zhuang), Proc. Amer. Math. Soc. 143 (2015), no. 11, 4633--4645.

Homological algebra, DG algebras, and related topics

On the finite generation of the cohomology of bosonizations, (with N. Andruskiewitsch, D. Jaklitsch, V. C. Nguyen, A. Oswald, J. Plavnik, and A. V. Shepler), J. Algebra, 691 (2026), 741–780.

Homological properties of 3-dimensional DG Sklyanin algebras, (with X.-F. Mao, H. Wang, Y.-N. Yang and M.-Y. Zhang), J. Algebra Appl., 23 (2024), no. 13, Paper No. 2450230, 35 pp.

Calabi-Yau property of quantum groups of $GL(2)$ representation type, (wth X.-L. Yu), J. Algebra Appl. 22 (2023), no. 6, Paper No. 2450104, 28 pp.

DG algebra structures on the quantum affine $n$-space $\mathcal O_{-1}(k^n)$, (with X.-F. Mao and M.-Y. Zhang), J. Algebra 594 (2022), 389--482.

New approaches to finite generation of cohomology rings, (with V. Nguyen and S. Witherspoon), J. Algebra 587 (2021), 390--428.

DG Poisson adjoint action and its application, (with X.-J. Li, X.-G. Hu, J.-F. Lu), Eur. J. Pure Appl. Math. 12 (2019), no.1, 14--24.

Finite generation of some cohomology rings via twisted tensor product and Anick resolutions, (with V. Nguyen and S. Witherspoon), J. Pure Appl. Algebra 223 (2019), 316--339.

DG Poisson algebra and its universal enveloping algebra, (with J.-F. Lu and G. Zhuang), Sci. China Math. 59 (2016), no. 5, 849--860.

Preprints and works in progress

Relative Dixmier property for Poisson algebras, (with H. Huang, Z. Nazemian, X. Tang, Y. Wang, J. J. Zhang), preprint (2026), arXiv:2601.18249.

Quantum-symmetric equivalence for superpotential algebras, (with H. Huang, V. Nguyen, K. Vashaw and P. Veerapen), preprint (2025), arXiv:2507.05612.

Hopf actions on Poisson algebras, (with A. Alqahtani and J. Gaddis), preprint (2025), arXiv:2506.06135.

Valuation method for Nambu-Poisson algebras, (with H. Huang, X. Tang, and J. J. Zhang), preprint (2023), arXiv:2312.00958.

Regular algebras of dimension four associated to coordinate rings of rank-two quadrics, (with R. Chandler, H. Tran, and P. Veerapen), preprint (2024), arXiv:2406.12737.

Zoom talk on V Non-Associative Day

Page updated

Google Sites

Report abuse