Refereed publications

1. (with A. M. Cohen), Lie algebraic computation Com. Phys. Comm. 97:53--62 (1996).
2. (with G. Ivanyos and L. R\'{o}nyai) Computing Cartan Subalgebras of Lie Algebras Applicable Algebra in Engineering Communication and Computing , 7:339--349 (1996).
3. (with G. Ivanyos, A. K\"{u}ronya and L. R\'{o}nyai), Computing Levi Decompositions of Lie Algebras, Applicable Algebra in Engineering Communication and Computing 8:291--303 (1997).
4. (with A. M. Cohen and L. R\'{o}nyai), 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 J. 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 G. 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 W. 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(g)-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 M. Harrison, J. Pilnikova, and J. 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 K. Baur and J. Draisma) Secant dimensions of minimal orbits: computations and conjectures, Experimental Mathematics , 16, no. 2, 239--250 (2007).
22. (with C. Fieker) Finding linear dependencies of algebraic numbers and algebraic Lie algebras, LMS JCM, 10 271--287, (2007).
23. (with S. Cicalo) 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).
    • Programs: nilpotent-orbit.html .
25. (with J. Pilnikova and J. Schicho) Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras, Journal of Symbolic Computation , 44 1--14 (2009).
26. (with S. Cicalo) 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).

Thesis

Books

1. Lie Algebras: Theory and Algorithms , North Holland Mathematical Library 56, Elsevier Science (2000).
   
   The index of this book is wrong. Here is a new version:
   • index.ps.gz (postscript),
   • index.pdf (pdf).
2. (with Serena Cicalò) Teoria di Galois, Aracne Editrice, 2008. (in italian)

Preprints

• Computing representatives of nilpotent orbits of theta-groups, http://arxiv.org/abs/0905.3149.