Books

1. Lie Algebras: Theory and Algorithms , North Holland Mathematical Library 56, Elsevier Science (2000).
2. (with Serena Cicalò) Teoria di Galois, Aracne Editrice, 2008. (in italian)
3. Computation with Linear Algebraic Groups , CRC Press, 2017.

Papers

1. (with Arjeh M. Cohen), Lie algebraic computation Com. Phys. Comm. 97:53--62 (1996).
2. (with Gábor Ivanyos and Lajos Rónyai) Computing Cartan Subalgebras of Lie Algebras Applicable Algebra in Engineering Communication and Computing , 7:339--349 (1996).
3. (with Gábor Ivanyos, Alex Küronya and Lajos Rónyai), Computing Levi Decompositions of Lie Algebras, Applicable Algebra in Engineering Communication and Computing 8:291--303 (1997).
4. (with Arjeh M. Cohen and Lajos Rónyai), Computations in finite-dimensional Lie algebras, Discrete Mathematics & Theoretical Computer Science 1: 129-138 (1997).
5. Calculating the structure of a semisimple Lie algebra J. of Pure and Applied Algebra , 117&118: 319-329 (1997).
6. An Algorithm for the Decomposition of Semisimple Lie Algebras J. of Theoretical Computer Science 187:117-122 (1997).
7. Constructing Faithful Matrix Representations of Lie Algebras in Proceedings of ISSAC97 , W. W. K\"uchlin ed., (1997).
   • issac97.ps.gz (47 kB).
8. Using Cartan subalgebras to calculate nilradicals and Levi subalgebras of Lie algebras, J. Pure And Applied Algebra 139: 25-39 (1999).
9. (with Jürgen Wisliceny) Constructing bases of finitely presented Lie algebras using Groebner bases in free algebras, Proceedings of ISSAC99 S. Dooley ed., (1999).
   • issac99.ps.gz (76 kB).
10. (with Gábor Ivanyos) Finding splitting elements and maximal tori in matrix algebras, Proceedings of the Euroconference on Interactions between Ring Theory and Representations of Algebras F. Van Oystaeyen and M. Saorin ed. 95-105 Marcel Dekker (2000).
    • torus.ps.gz (71 kB).
11. Constructing representations of split semisimple Lie algebras, J. Pure And Applied Algebra 164: 87-107 (2001).
    • conrep.ps.gz (119 kB).
12. Computing with quantized enveloping algebras: PBW-type bases, highest-weight modules, R-matrices, Journal of Symbolic Computation 32: 475-490 (2001).
    • qalg.ps.gz (81 kB).
13. (with Werner Nickel) Constructing faithful representations of finitely-generated torsion-free nilpotent groups, Journal of Symbolic Computation 33: 31-41 (2002).
    • nilrep.ps.gz (59 kB).
14. Constructing canonical bases of quantized enveloping algebras, Experimental Mathematics 11: 161-170 (2002).
    • canbas.ps.gz (74kB).
15. An algorithm to compute the canonical basis of an irreducible U_q(𝕬)-module, The LMS JCM, 6:105-118 (2003).
    • tensor.ps.gz (66 kB).
16. Five constructions of representations of quantum groups Note di Matematica, 22:27--48 (2003/04).
    • modcons.ps.gz (86 kB).
17. Constructing homomorphisms between Verma modules, Journal of Lie Theory, 15:415--428 (2005).
    • verma.ps.gz (135 kB).
18. Classification of solvable Lie algebras Experimental mathematics, 14, no. 1, 15--25 (2005).
    • lieclass.ps.gz (66 kB).
19. (with Michael Harrison, Jana Pílniková, and Josef Schicho) A Lie algebra method for rational parametrization of Severi-Brauer surfaces, http://arxiv.org/abs/math.AG/0501157 , Journal of Algebra , 303, 514--529 (2006).
20. Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, Journal of Algebra, 309 (2), 640-653 (2007). For a more detailed version: http://arxiv.org/abs/math.RA/0511668 .
21. (with Karin Baur and Jan Draisma) Secant dimensions of minimal orbits: computations and conjectures, Experimental Mathematics , 16, no. 2, 239--250 (2007).
22. (with Claus Fieker) Finding linear dependencies of algebraic numbers and algebraic Lie algebras, LMS JCM, 10 271--287, (2007).
23. (with Serena Cicalò) Nonassociative Groebner bases, finitely-presented Lie rings, and the Engel condition, Proceedings of ISSAC07 C. Brown ed., (2007).
    • issac07.pdf
24. Computing with nilpotent orbits in simple Lie algebras of exceptional type , LMS JCM, 11, 280--297, (2008).
    • Erratum: ernilpo.pdf .
25. (with Jana Pílniková and Josef Schicho) Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras, Journal of Symbolic Computation , 44 1--14 (2009).
26. (with Serena Cicalò) Nonassociative Groebner bases, finitely-presented Lie rings, and the Engel condition II, Journal of Symbolic Computation, 44 786--800 (2009).
27. Constructing algebraic groups from their Lie algebras, Journal of Symbolic Computation , 44, 1223--1233, (2009).
28. (with Andrea Pavan) Constructing arithmetic subgroups of unipotent groups, http://arxiv.org/abs/0806.4916 , Journal of Algebra, 322 3950--3970 (2009).
29. (with Dietrich Burde and Bettina Eick) Computing faithful representations for nilpotent Lie algebras http://arxiv.org/abs/0807.2345 , Journal of Algebra, 322 602--612 (2009).
30. (with Alexander Elashvili) Induced nilpotent orbits of the simple Lie algebras of exceptional type, http://arxiv.org/abs/0905.2743 , Georgian Mathematical Journal , 16 257--278 (2009).
    • Erratum: erinduced.pdf .
31. Constructing semisimple subalgebras of semisimple Lie algebras, http://arxiv.org/abs/1004.1972 , Journal of Algebra, 325 416--430 (2011).
32. Computing representatives of nilpotent orbits of θ-groups, http://arxiv.org/abs/0905.3149, Journal of Symbolic Computation, 46, 438--458 (2011).
33. (with Lorenzo Fortunato) Angular momentum non conserving symmetries in bosonic models, http://arxiv.org/abs/1102.4698 , J. Phys. A: Math. Theor. 44, 145206 (2011).
34. (with Lorenzo Fortunato) "Lost chains" in algebraic models, J. Phys.: Conf. Ser. 284 012025 (2011).
35. (with Serena Cicalò and Csaba Schneider) Six-dimensional nilpotent Lie algebras, http://arxiv.org/abs/1011.0361 , Lin. Alg. Appl., 436, 163--189 (2012).
36. (with Serena Cicalò and Michael Vaughan-Lee) An effective version of the Lazard correspondence, Journal of Algebra, 352, 430--450 (2012).
37. (with Oksana Yakimova) Good index behaviour of θ-representations, I, http://arxiv.org/abs/1003.4162 , Algebras and Rep. Th., 15, 613--638 (2012).
38. (with Ernest Vinberg and Oksana Yakimova) An effective method to compute closure ordering for nilpotent orbits of θ-representations, http://arxiv.org/abs/1107.1864 , Journal of Algebra, 371, 38--62 (2012).
39. (with Paolo Faccin and Wilhelm Plesken) Computing generators of the unit group of an integral abelian group ring, Journal of Algebra, 373, 441--452 (2013).
40. (with Dietrich Burde) Classification of Novikov algebras, http://arxiv.org/abs/1106.5954 , Applicable Algebra in Engineering Communication and Computing , 24, 1--15 (2013).
41. (with Heiko Dietrich and Paolo Faccin) Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras, Journal of Symbolic Computation, 56, 27--45, (2013).
42. (with Heiko Dietrich) A computational approach to the Kostant-Sekiguchi correspondence, http://arxiv.org/abs/1209.560 , Pacific Journal of Mathematics, 265(2), 349--379, (2013).
43. (with Francesco Oriente) Classifying semisimple orbits of θ-groups, Mathematics of Computation, 83(289), 2509--2526, (2014).
44. (with Heiko Dietrich and Paolo Faccin) A GAP package for computing with real semisimple Lie algebras. In H. Hong and C. Yap (Eds.): ICMS 2014, LNCS 8592, pp. 59--66. Springer, Heidelberg, 2014.
45. (with Alla Detinko and Dane Flannery) Integrality and arithmeticity of solvable linear groups, Journal of Symbolic Computation, 68, 138--145, (2015).
46. (with Heiko Dietrich and Paolo Faccin) Regular subalgebras and nilpotent orbits of real graded Lie algebras, http://arxiv.org/abs/1407.7850 , Journal of Algebra, 423, 1044--1079, (2015).
47. (with Paolo Faccin) Constructing semisimple subalgebras of real semisimple Lie algebras. Lie algebras and related topics, 75--89, Contemp. Math., 652, Amer. Math. Soc., Providence, RI, 2015.
48. (with Heiko Dietrich, Daniele Ruggeri and Mario Trigiante) Nilpotent orbits in real symmetric pairs and stationary black holes, Fortschritte der Physik 65 (2), DOI: 10.1002/prop.201600118 (2017).
49. Classification of nilpotent associative algebras of small dimension, http://arxiv.org/abs/1009.5339, Internat. J. Algebra Comput. 28, no. 1, 133--161 (2018).
50. (with Alla Detinko) 2-generation of simple Lie algebras and free dense subgroups of algebraic groups https://arxiv.org/abs/1905.01853 , Journal of Algebra, 545, 159--173, (2020).
51. (with Alessio Marrani) Real forms of embeddings of maximal reductive subalgebras of the complex simple Lie algebras of rank up to 8 https://arxiv.org/abs/1911.06575 J. Phys. A: Math. Theor. doi.org/10.1088/1751-8121/ab7c8c (2020).
52. (with Heiko Dietrich) Computing the real Weyl group, Journal of Symbolic Computation, 104, 1--14 (2021).
53. (with Sajid Ali, Hassan Azad, Indranil Biswas) A constructive method for decomposing real representations https://arxiv.org/abs/1804.03614, Journal of Symbolic Computation, 104, 328--342 (2021).
54. (with Andrew Douglas) Closed subsets of root systems and regular subalgebras https://arxiv.org/abs/1901.08122, Journal of Algebra, 565, 531--547 (2021).
55. (with Mikhail Borovoi and Hông Vân Lê) Classification of real trivectors in dimension nine, Journal of Algebra 603 118--163 (2022), https://arxiv.org/abs/2108.00790 .
56. (with Heiko Dietrich, Alessio Marrani and Marcos Origlia) Classification of four qubit states and their stabilisers under SLOCC operations, Journal of Physics A 55 no. 9, Paper No. 095302 (2022), https://arxiv.org/abs/2111.05488 .
57. (with Heiko Dietrich, Alessio Marrani and Marcos Origlia) Classification of four-rebit states J. Geom. Phys. 179, Paper No. 104610, (2022), https://arxiv.org/abs/2201.11777 .
58. (with Sabino Di Trani and Alessio Marrani), Classification of real and complex three-qutrit states J. Math. Phys. 64 no. 9, Paper No. 091701 (2023), https://arxiv.org/abs/2305.01270 .
59. Exploring Lie theory with GAP Computational Aspects of Discrete Subgroups of Lie Groups, Contemp. Math., 783, 27--46 (2023), https://arxiv.org/abs/2303.15927 .
60. (with Mikhail Borovoi and Bodgan Adrian Dina), Real non-degenerate two-step nilpotent Lie algebras of dimension eight Eur. J. Math. 10 no. 1, Paper No. 16 (2024), https://arxiv.org/abs/2308.11413 .
61. (with Heiko Dietrich) A computational approach to almost-inner derivations, Journal of Symbolic Computation, 125, Paper No. 102312, (2024), https://arxiv.org/abs/2403.05905 .
62. (with Mikhail Borovoi), Computing Galois cohomology of a real linear algebraic group J. Lond. Math. Soc. 109 no. 5, Paper No. e12906, (2024), https://arxiv.org/abs/2308.04962 .
63. (with Maciej Bochenski, Piotr Jastrzebski and Aleksy Tralle) Non-virtually abelian discontinuous group actions vs. proper SL(2,R)-actions on homogeneous spaces Experimental Mathematics, to appear, https://arxiv.org/abs/2206.01069 .

Thesis

Preprints

• Computations with nilpotent orbits in SLA, http://arxiv.org/abs/1301.1149 .
• (with Mikhail Borovoi and Hông Vân Lê) Real graded Lie algebras, Galois cohomology, and classification of trivectors in R^9, https://arxiv.org/abs/2106.00246 .
• (with Mikhail Borovoi) Computing Galois cohomology of a real linear algebraic group https://arxiv.org/abs/2308.04962.