Research and Publications
Research.
My past research revolves mostly around algebraic and geometric structures that appeared in mathematical physics.
In the algebraic part, I was interested in Rota-Baxter operators on algebras (which are the operator analogue of classical Yang-Baxter solutions in mathematical physics), homotopy algebras and deformation theory.
In the geometric part, I was interested in Poisson structures on manifolds (geometric formulation of classical Yang-Baxter solutions) and their interactions with the Lie theory of groupoids - algebroids.
More details can be found soon.
Publications.
[] Cup product, Frolicher-Nijenhuis bracket and the derived bracket associated to Hom-Lie algebras (with A. Baishya), In preparation.
[] Diassociative conformal algebras and their cohomology (with A. Sahoo), In preparation.
[] Quasi-infinitesimal bialgebras and Rota-Baxter quasi-Nijenhuis structures, In preparation.
[] Averaging operators on n-Lie algebras, n-racks and a higher analogue to the set-theoretical solution of the Yang-Baxter equation, In preparation.
[] Rota-Baxter Leibniz bialgebras (with R. Mandal), In preparation.
[] Matched pairs, Manin triples of relative Rota-Baxter Lie algebras and associated bialgebra theory (with R. Mandal), In preparation.
[] Nijenhuis deformations of Poisson algebras and F-manifold algebras (with A. Baishya), Submitted.
[] Averaging operators on groups, racks and Leibniz algebras, Submitted.
[] Representations and cohomology of a matched pair of Lie algebras, and L_infinity-algebras (with A. Baishya), submitted.
[] Non-abelian cohomology of Lie H-pseudoalgebras and inducibility of automorphisms, submitted.
[] Higher structures for Lie H-pseudoalgebras, submitted.
[] Poisson dialgebras (with S. K. Mishra and G. Mukherjee), submitted.
[] Homotopification and categorification of Leibniz conformal algebras (with A. Sahoo), submitted.
[] Homotopy conformal algebras (with A. Sahoo), submitted.
[] Averaging algebras of any nonzero weight (with R. Mandal), submitted.
[] Embedding tensors on Hom-Lie algebras (with A. Makhlouf), submitted.
[] Controlling structures, deformations and homotopy theory for averaging algebras, submitted.
[] A cohomological study of modified Rota-Baxter algebras, submitted.
[] A unified extension theory of Rota-Baxter algebras, dendriform algebras, and a fundamental sequence of Wells (with N. Rathee), submitted.
[] Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators, submitted.
[] Deformations and homotopy theory for Rota-Baxter family algebras, J. Algebra Appl. to appear.
[] Compatible, split and family Loday algebras, revision submitted.
[] Matching relative Rota-Baxter algebras, matching dendriform algebras and their cohomologies (with R. Mandal), Comm. Algebra to appear.
[] Extension, deformation and categorification of AssDer pairs (with A. Mandal), revision submitted.
[47] Pre-Leibniz algebras, Comm. Algebra 52 (2024), 3383-3399. [article]
[46] L_infinity-structures and cohomology theory of compatible O-operators and compatible dendriform algebras (with S. Guo and Y. Qin), J. Math. Phys. 65 (2024), 031701. [article]
[45] Cohomology and deformations of generalized Reynolds operators on Leibniz algebras (with S. Guo), Rocky Mountain J. Math. 54 (1) (2024), 161-178. [article]
[44] (Co)homology of compatible associative algebras (with T. Chtioui and S. Mabrouk), Comm. Algebra Vol. 52, Issue 2 (2024) 582-603. [article]
[43] 2-term averaging L_infinity-algebras and non-abelian extensions of averaging Lie algebras (with S. Sen), J. Algebra 644 (2024) 126-151. [article]
[42] Relative Rota-Baxter Leibniz algebras, their characterization and cohomology, Linear Multilinear Algebra Vol. 71, Issue 17 (2023) 2796-2822. [article]
[41] Weighted relative Rota-Baxter operators on Leibniz algebras and Post-Leibniz algebra structures, Publ. Math. Debrecen 103, Issue 3-4 (2023) 385-406. [article]
[40] Bimodules over relative Rota-Baxter algebras and cohomologies (with S. K. Mishra), Algebr. Represent. Theory 26 (2023) 1823-1848. [article]
[39] Cohomology of Lie algebra morphism triples and some applications, Math. Phys. Anal. Geom. Vol. 26 (2023) Article no. 26. [article]
[38] Extensions and automorphisms of Rota-Baxter groups (with N. Rathee), J. Algebra 636 (2023) 626-665. [article]
[37] Diassociative family algebras and averaging family operators (with S. Sen), J. Geom. Phys. 193 (2023) 104964. [article]
[36] Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms (with S. K. Hazra and S. K. Mishra), Linear Algebra Appl. 669 (2023) 147-174. [article]
[35] Cohomology and deformations of compatible Hom-Lie algebras, J. Geom. Phys. 192 (2023) 104951. [article]
[34] Relative Rota-Baxter systems on Leibniz algebras (with S. Guo), J. Korean Math. Soc. 60 (2023), No. 2, pp. 303-325. [article]
[33] Twisted Rota-Baxter families and NS-family algebras, J. Algebra 612 (2022) 577-615. [article]
[32] Cohomology and deformations of weighted Rota-Baxter operators, J. Math. Phys. Vol. 63, Issue 9 (2022) 091703. [article]
[31] Compatible L-infinity algebras, J. Algebra 610 (2022) 241-269. [article]
[30] The L_infinity-deformations of associative Rota-Baxter algebras and homotopy Rota-Baxter operators (with S. K. Mishra), J. Math. Phys. Vol. 63, Issue 5 (2022) 051703. [article]
[29] Cohomology and deformations of twisted Rota-Baxter operators and NS-algebras, J. Homotopy Relat. Struct. 17 (2022) 233-262. [article]
[28] Noncommutative differential calculus structure on secondary Hochschild (co)homology (with S. K. Mishra and A. Naolekar), Comm. Algebra Vol. 50, Issue 6 (2022) 2349-2365. [article]
[27] Cohomology and deformations of crossed homomorphisms, Bull. Belgian Math. Soc. Simon Stevin Vol. 28, Issue 3 (2022) 381-397. [article]
[26] Cohomology and deformations of dendriform algebras, and Dend-infinity algebras, Comm. Algebra Vol. 50, Issue 4 (2022) 1544-1567. [article]
[25] Crossed extensions of Lie algebras, J. Lie Theory 32 (2022), No. 2, 313-326. [article]
[24] Cohomology of BiHom-associative algebras, J. Algebra Appl. Vol. 21, No. 01, 2250008 (2022). [article]
[23] Nijenhuis operators on Hom-Lie algebras (with S. Sen), Comm. Algebra Vol. 50, Issue 3 (2022) 1038-1054. [article]
[22] Extensions and deformations of algebras with higher derivations, Bull. Malays. Math. Sci. Soc. 45 (2022) 379-398. [article]
[21] Rota-Baxter operators on involutive associative algebras, Acta Sci. Math. (Szeged) 87 (2021), 349-366. [article]
[20] Twisted Rota-Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras, J. Math. Phys. Vol. 62, Issue 9 (2021) 091701. [article]
[19] Involutive and oriented dendriform algebras (with R. Saha), J. Algebra 581 (2021) 63-91. [article]
[18] Leibniz algebras with derivations, J. Homotopy Relat. Struct. 16 (2021) 245-274. [article]
[17] Noncommutative differential calculus on (co)homology of hom-associative algebras, Comm. Algebra Vol. 49, Issue 5 (2021) 2199-2208. [article]
[16] Contact Courant algebroids and L-infinity algebras, J. Geom. Phys. 163 (2021) 104127. [article]
[15] On equivariant dendriform algebras (with R. Saha), Colloq. Math. 164 (2021), 283-303. [article]
[14] Deformations of Loday-type algebras and their morphisms, J. Pure Appl. Algebra Vol. 225, Issue 6 (2021) 106599. [article]
[13] Cohomology and deformations of hom-dendriform algebras and coalgebras, Colloq. Math. Vol. 163, no. 1 (2021), 37-52. [article]
[12] Multiplicative Nambu structures on Lie groupoids, J. Ramanujan Math. Soc. 35 (2020), no. 3, 277-298. [article]
[11] Deformations of associative Rota-Baxter operators, J. Algebra 560 (2020) 144-180. [article]
[10] Hom-associative algebras up to homotopy, J. Algebra 556 (2020) 836-878. [article]
[09] Gerstenhaber algebra structure on the cohomology of a hom-associative algebra, Proc. Indian Acad. Sci. (Math. Sci.) 130 (2020), no. 1, Paper No. 20. [article]
[08] Poisson-Nijenhuis groupoids, Rep. Math. Phys. 84 (2019), no. 3, 303-331. [article]
[07] Nambu structures on Lie algebroids and their modular classes (with S. Gondhali and G. Mukherjee), Proc. Indian Acad. Sci. (Math. Sci.) Vol. 129 (2019), no. 4, Art. 59. [article]
[06] Gauge transformations of Jacobi structures and contact groupoids, Math. Phys. Anal. Geom. Vol. 22 (2019), no. 1. [article]
[05] Nambu structures and associated bialgebroids (with S. Basu, S. Basu and G. Mukherjee), Proc. Indian Acad. Sci. (Math. Sci.) Vol. 129 (2019), no. 1, Art. 12, 36 pp. [article]
[02] Singular reduction of Nambu-Poisson manifolds, Int. J. Geom. Methods Mod. Phys. 14, 1750128 (2017) 13 pp. [article]
[01] On generalized Lie bialgebroids and Jacobi groupoids, Extracta Mathematicae Vol. 31, Num. 2, 199-225 (2016). [article]