Publications

• As this website is determined to become outdated, more updated versions of the publication list, as well as free pdf-preprint versions of all papers can be found on arXiv, Google Scholar, Researchgate and DI-fusion.
• Preprints
  P. Saracco and J. Vercruysse, Geometric partial comodules over flat coalgebras in Abelian categories are globalizable, arXiv:2107.07299
  M. D'Adderio, W. Hautekiet, P. Saracco and J. Vercruysse, Partial and global representations of finite groups, arXiv:2005.09465
  P. Saracco and J. Vercruysse, Globalizations of geometric partial actions, arXiv:2001.07669.
• Accepted for publication/in press
  P. Saracco and J. Vercruysse, On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras, arXiv:2107.06574, accepted for publication in Semigroup Forum. 
  A. Agore, A. Gordienko and J. Vercruysse, V-universal Hopf algebras (co)acting on Ω-algebras, arXiv:2005.12954, to appear in Communications in Contemporary Mathematics.
  
• Published
  [33] M. Buckley, T. Fieremans, C. Vasilakopoulou, J. Vercruysse, Oplax Hopf algebras. High. Struct. 5 (2021), no. 1, 71–120.
  [32] A. Agore, A. Gordienko and J. Vercruysse, Equivalences of (co)module algebra structures over Hopf algebras. J. Noncommut. Geom. 15 (2021), no. 3, 951–993.
  [31] G. Böhm, J. Vercruysse, BiHom Hopf algebras viewed as Hopf monoids, Contemporary Mathematics 771 (2021), 1--41.
  [30] M.M.S. Alves, E. Batista, F. Castro, G. Quadros and J. Vercruysse, Partial corepresentations of Hopf algebras,  J. Algebra 577 (2021), 74–135. 
  [29] M. Buckley, T. Fieremans, C. Vasilakopoulou and J. Vercruysse, A Larson-Sweedler theorem for Hopf V-categories, Adv. Math. 376 (2021), 107456.
  [28] J. Hu and J. Vercruysse, Geometrically partial actions, Trans. Amer. Math. Soc., 373 (2020), 4085–4143.
  [27] M.M.S. Alves, E. Batista and J. Vercruysse, Dilations of partial representations of Hopf algebras, J. Lond. Math. Soc. 100 (2019), 273–300.
  [26] M. Gran, F. Sterck and J. Vercruysse, A semi-abelian extension of a theorem by Takeuchi, J. Pure Appl. Algebra 223 (2019), 4171–4190.
  [25] M. Gran, G. Kadjo and J. Vercruysse, Split extension classifiers in the category of cocommutative Hopf algebras, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), 355–382.
  [24] S. Caenepeel, E. Batista and J. Vercruysse, Hopf categories, Algebr. Represent. Theory, 19 (2016), 1173–1216.
  [23] M. Gran, G. Kadjo and J. Vercruysse, A Torsion Theory in the Category of Cocommutative Hopf Algebras, Appl. Categ. Structures, 24 (2016) 269–282.
  [22] E. Batista and J. Vercruysse, Dual constructions for partial actions of Hopf algebras, J. Pure Appl. Algebra 220 (2016), 518--559.
  [21] M.M.S. Alves, E. Batista and J. Vercruysse, Partial representations of Hopf algebras, J. Algebra 426 (2015).
  [20] I. Goyvaerts and J. Vercruysse, Lie monads and dualities, J. Algebra 414 (2014), 120--158.
  [19] I. Goyvaerts and J. Vercruysse, On the duality of generalized Lie and Hopf algebras, On the duality of generalized Lie and Hopf algebras, Adv. Math. 258 (2014), 154--190.
  [18] J. Vercruysse, Hopf algebras -- Variant notions and reconstruction theorems, in ``Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse'', C. Heunen, M. Sadrzadeh, E. Grefenstette (eds.). Oxford University Press, Oxford, 2013, 115--145.
  [17] I. Goyvaerts and J. Vercruysse, A note on the categorisation of Lie algebras, in ``Lie Theory and its applications in physics IX'', V. Dobrev (eds.), Spring Proceedings in Mathematics and Statistics 36, Springer, Tokyo, 2013, 541--550.
  [16] T. Brzezinski, A. Vazquez Marquez and J. Vercruysse, The Eilenberg-Moore category and a Beck-type theorem for a Morita context, Appl. Categorical Structures 19, (2011), 821--858.
  [15] K. Janssen and J. Vercruysse, Multiplier Hopf and bi-algebras, J. Algebra Appl. 9 (2), (2010), 275 -- 303.
  [14] F. Castaño Iglesias, C. Nastasescu, J. Vercruysse, Quasi-Frobenius functors. Applications, Comm Algebra, 38 (8), (2010), 3057-3077.
  [13] G. Böhm and J. Vercruysse, Morita theory for comodules over corings, Comm Algebra. 37 (9), (2009), 3207 -- 3247.
  [12] T. Brzezinski and J. Vercruysse, Bimodule Herds, J. Algebra, 321 (9), (2009), 2670--2704.
  [11] L. El Kaoutit and J. Vercruysse, Cohomology for Bicomodules. Separable and Maschke Functors, Journal of K-theory, 3 (1) (2009), 123--152.
  [10] J. Vercruysse, Quasi-co-Frobenius corings as Galois comodules, Arabian Journal for Science and Engeneering, 22 (2C) (2008), 529--552.
  [9] J. Vercruysse, Equivalences between categories of Modules and categories of Comodules, Acta Math. Sin. (Engl. Ser.) 24 (10) (2008), 1655--1674.
  [8] M. Iovanov and J. Vercruysse, Cofrobenius Corings and adjoint Functors, Journal of Pure and Applied Algebra, 212 (9), 2027-2058 (2008).
  [7] J. Gómez-Torrecillas and J. Vercruysse, Comatrix Corings and Galois Comodules over firm rings, Algebras and Representation Theory, 10 (3) (2007), 271--306.
  [6] G. Böhm and J. Vercruysse, Morita theory for Coring extensions and Cleft bicomodules, Advances in Mathematics 209 (2007), 611--648. Corrigendum, Advances in Mathematics 221 (2009), 682--686.
  [5] S. Caenepeel, E. De Groot and J. Vercruysse, Galois theory for Comatrix Corings: Descent theory, Morita theory, Frobenius and separability properties, Trans. Amer. Math. Soc. 359 (2007), 185--226.
  [4] S. Caenepeel, E. De Groot and J. Vercruysse, Constructing Infinite Comatrix Corings from Colimits, Appl. Categorical Structures, 14 (2006), 539--565.
  [3] J. Vercruysse, Local units versus local projectivity. Dualisations : Corings with local structure maps, Communications in Algebra 34 (2006), 2079--2103.
  [2] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Rationality properties for Morita contexts associated to corings, in ``Hopf algebras in non-commutative geometry and physics", Caenepeel S. and Van Oystaeyen, F. (eds.), Lect. Notes Pure Appl. Math., Dekker, New York (2005) 113--136.
  [1] S. Caenepeel, J. Vercruysse and Shuanhong Wang, Morita Theory for corings and cleft entwining structures, Journal of Algebra 276 (2004) 210--235.
• Edited volumes
  S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories”, Bull. Belgian Math. Soc. - Simon Stevin 23 (2016) issue 5, ISSN 1370-1444.
  S. Caenepeel, M. Gran, J. Vercruysse, Y. Zhang (eds.), “New trends in Hopf algebras and tensor categories (Part II)”, Bull. Belgian Math. Soc. - Simon Stevin 24 (2017) issue 1, ISSN 1370-1444.