12. (With S. Bera, Snehashis Mukherjee and Sugata Mandal) Bernstein-type inequalities for quantum algebras, arXiv:2501.11399
11. (With Sugata Mandal) A note on certain determinants arising from a Galois extension (in preparation)
10. Ashish Gupta; Sugata Mandal. Skew-Forms and Galois Theory. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1337-1347. doi : 10.5802/crmath.645. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.645/
9. (with S. Mandal), On the automorphisms of quantum $n$-spaces and quantum $n$-tori, Beitr Algebra Geom (2024). https://doi.org/10.1007/s13366-024-00760-z
8. (With P.N. Shivkumar and Y. Zhang) On Zeros of polynomials and some infinite series with some bounds, accepted for publication in Dynamic systems and applications, 2023.
7. (with Umamaheshwaran Arunachalam) GK dimensions of simple modules over twisted group algebras $k \ast A$ , Izvestiya Mathematics, 2022, Volume 86, Issue 4, Pages 715–726
6. (with Sarkar A. D) A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings, Algebras and Representation Theory, June 2018, Volume 21, Issue 3, pp 579–587.
Summary : The Gelfand–Kirillov dimension is an important tool in the study of non-commutative infinite dimensional algebras and their modules. We show a dichotomy for the Gelfand–Kirillov dimension of simple modules over certain simple rings of differential operators. We thus answer a question of J. C. McConnell in Representations of solvable Lie algebras V. On the Gelfand-Kirillov dimension of simple modules. McConnell (J. Algebra 76(2), 489–493, 1982) concerning this dimension for a class of algebras that arise as simple homomorphic images of solvable lie algebras. We also determine the Gelfand–Kirillov dimension of an induced module.
5. The Krull and global dimension of the tensor product of quantum tori Journal of Algebra and its Applications, Volume 15, Issue 09, 2016.
Summary : In this paper we determine the inequalities that give upper bounds on the the Krull and global dimensions of the (algebra) tensor products of quantum tori. The geometric invariant of C.J.B. Brookes and J. R. J. Groves is used the proof.
4. Representations of the $n$ dimensional quantum torus, Communications in Algebra, Volume 44, Issue 7, 2016.
Summary: We prove an inequality for the Gelfand-Kirillov dimension of the irreducible representations of quantum tori. This dimension is gaining importance as a tool in the study of non-commutative algebras and their representations.
3. On a Conjecture of Groves for Modules Over Infinite Nilpotent Groups, Communications in Algebra, Volume 42, Issue 4, April 2014, pages 1682-1689
Summary: We show that a conjecture of Groves for modules over nilpotent groups of class 2 holds for the codimension 2 case with certain assumptions.
2. GK Dimensions of Simple Modules Over K[X ±1, σ], Communications in Algebra, Volume 41, Issue 7, May 2013, pages 2593-2597.
Summary: We determine exactly the values for the GK dimension of simple modules over a skew-Laurent extension of the Laurent polynomial ring.
Modules over quantum Laurent polynomials, Journal of Australian Math. Soc., 91 (3), pages 323--341.
Summary: We prove non-commutative versions of certain important results concerning a geometric invariant introduced to give a geometric criterion for when a meta-abelian group is finitely presented. Using this geometric invariant it is shown that a quantum tori possessing a strongly-holonomic module have the form of a tensor product of 2-dimensional quantum tori. Strongly holonomic modules arise, for example, from impervious modules We also apply these results for proving addition theorems for the GK dimensions of modules over quantum Laurent polynomials. Also non-holonomic simple modules over quantum Laurent polynomials were shown to exist and a recipe was given for their construction.