Mathematical Foundations of Computer Science: Category Theory and Logic within Computer Science: theory of coalgebras and the associated abstract modal logic, Stone duality, enriched category theory, monads.
Non-Commutative Algebra: Hopf algebras, quantum groups and categorical generalisations.
A. Tănăsescu, A. Balan, P. G. Popescu. Zero-correlation entanglement vs. Schmidt rank, The European Physical Journal Plus 136, 476 (2021) (link)
A. Balan, A. Kurz. An Equational Approach to Enriched Distributivity, Revue Roumaine de Mathématiques Pures et Appliquées 66(3-4):577-596 (2021) (link)
A. Balan, A. Kurz, J. Velebil. Extensions of Functors to V-Cat, Logical Methods in Computer Science 15(1):1-57 (2019) (online)
A. Balan. On Hopf adjunctions, Hopf monads and Frobenius-type properties, Applied Categorical Structures 25(5):747-774 (2017) (link) (arXiv 1411.2236)
A. Balan, A. Kurz, J. Velebil. An Institutional Approach to Positive Coalgebraic Logics, Journal of Logic and Computation 7(6):1799-1824 (2017) (link)
A. Balan, A. Kurz, J. Velebil. Some aspects of positive coalgebraic logic. In: Duality in Computer Science, Dagstuhl Reports vol. 5(10) (2016)
A. Balan, A. Kurz, J. Velebil. Extensions of functors from Set to V-cat. In: Proceedings of the 6th
International Conference on Algebra and Coalgebra in Computer Science CALCO2015, LIPIcs 2015, 16-32 (online)
A. Balan, A. Kurz, J. Velebil. Positive Fragments of Coalgebraic Logics, Logical Methods in Computer Science 11(3:18), 1-51, 2015 (online)
A. Balan. A note on Frobenius monoidal functors on autonomous categories, preprint 2014 (arXiv 1407.1012)
A. Balan, A. Kurz, J. Velebil. An Institutional Approach to Positive Coalgebraic Logic. In: R. Diaconescu, I. Tutu, M. Codescu (eds.), Technical report on the 22nd International Workshop on Algebraic Development Techniques WADT 2014, 7(2014) Preprint Series of the Institute of Mathematics of the Romanian Academy, ISSN 0250 3638, p.20-21 (available link)
A. Balan. On biproducts and terminal coalgebras, U.P.B. Sci. Bull. Series A 76(2), 285-294, 2014 (link)
A. Balan, A. Kurz, J. Velebil. Positive Fragments of Coalgebraic Logics. In: R. Heckel, S. Milius, (eds.), 5th
International Conference on Algebra and Coalgebra in Computer Science
CALCO2013, LNCS 8089, Springer 51-65, 2013 (link) (pdf)
A. Balan, A. Kurz, J. Velebil. On Coalgebraic Logic over Posets
. In: L. Schroeder, D. Pattinson (eds.), Short Contributions of 11th International Workshop CMCS 2012, Inst. Cybern.,
Technical University Tallin, 6-7, 2012 (pdf)
A. Balan, A. Kurz. Finitary functors: from Set to Preord and Poset
. In: A. Corradini, B. Klin, C. Cîrstea (eds.), 4th International Conference on Algebra and Coalgebra in
Computer Science CALCO2011, LNCS 6859, Springer, Heidelberg, 8
5-99, 2011 (link) (pdf)
A. Balan, A. Kurz. On coalgebras over algebras, Theor. Comput. Sci. 412(38) 4989-5005,
2011 (link) (pdf)
A. Balan. A Note on Enriched Categories, UPB Sci. Bull. Series A: Appl. Math. Phys. 72(4),
147-154, 2010 (link)
A. Balan, A. Kurz. On Coalgebras over Algebras. In: B. Jacobs, M. Niqui, J. Rutten and A.
Silva (eds.), 10th International Workshop on Coalgebraic Methods in Computer Science
CMCS 2010, Elect. Notes Theor. Comput. Sci., 264(2), 47-6
2, 2010 (link)
A. Balan. Galois Extensions for Coquasi-Hopf Algebras, Comm. Algebra, 38(4), 1491-1525, 2010 (link) (arXiv 0804.3046v1)
A. Balan. Yetter-Drinfeld Modules and Galois Extensions for Coquasi-Hopf Algebras, UPB Sci. Bull. Series A: Appl. Math. Phys., 71(3), 43-60, 2009 (link).
A. Balan. A Morita Context and Galois extensions for Quasi-Hopf Algebras, Comm. Algebra,
37(4), 1-22, 2009 (link) (arXiv 0705.3515v2)
A. Balan. Crossed Products and Cleft Extensions for Coquasi-Hopf Algebras
, Arabian J. Sci.
Eng., special issue "Interactions of Algebraic & Coalgebraic Structures (Theory and
Applications)", 33(2C), 53-84, 2008 (link)
A. Balan. Actions and coactions for (co)quasi-Hopf algebras (PhD Thesis, in Romanian), University of Bucharest (2007)
A. Balan. Integral Extensions of Module Algebras, UPB Sci. Bull. Series A: Appl. Math. Phys., 61(3-4) 67-76, 1999 (zbMATH)
A Morita context and Galois extensions for quasi-Hopf algebras, "New techniques in Hopf algebras and graded ring theory", Bruxelles (Belgium), Sept. 2006 (program)