Algebras – Non-Associative

  1. Vyacheslav A. Artamonov, Alexander A. Mikhalev, and Alexander V. Mikhalev, Combinatorial properties of free algebras of Schreier varieties, Polynomial identities and combinatorial methods (Pantelleria, 2001), Lecture Notes in Pure and Appl. Math., vol. 235, Dekker, New York, 2003, pp. 47–99.[MR]
  2. Y. Barnea and D. S. Passman, Filtrations in semisimple Lie algebras. II, Trans. Amer. Math. Soc. 360 (2008), no. 2, 801–817 (electronic).[MR]
  3. Laurent Bartholdi, Benjamin Enriquez, Pavel Etingof, and Eric Rains, Groups and Lie algebras corresponding to the Yang-Baxter equations, J. Algebra 305 (2006), no. 2, 742–764.[MR/arXiv]
  4. Antonio Behn, Alberto Elduque, and Alicia Labra, A class of locally nilpotent commutative algebras, preprint (2009), 12 pages.[arXiv]
  5. C. P. Bendel, D. K. Nakano, B. J. Parshall, and C. Pillen, Cohomology for quantum groups via the geometry of the Nullcone, Preprint (2007), 1–58.
  6. Christopher P. Bendel, Daniel K. Nakano, and Cornelius Pillen, Second cohomology groups for Frobenius kernels and related structures, Adv. Math. 209 (2007), no. 1, 162–197.[MR/link]
  7. Dietrich Burde, Bettina Eick, and Willem de Graaf, Computing faithful representations for nilpotent Lie algebras, J. Algebra 322 (2009), no. 3, 602–612.[MR/doi]
  8. A. Caranti, S. Mattarei, and M. F. Newman, Graded Lie algebras of maximal class, Trans. Amer. Math. Soc. 349 (1997), no. 10, 4021–4051.[MR]
  9. A. Caranti and M. F. Newman, Graded Lie algebras of maximal class. II, J. Algebra 229 (2000), no. 2, 750–784.[MR]
  10. Serena Cicalò and Willem A. de Graaf, Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition: II, J. Symbolic Comput. 44 (2009), no. 7, 786–800.
  11. Arjeh M. Cohen and Dan Roozemond, Computing Chevalley bases in small characteristics, J. Algebra 322 (2009), no. 3, 703–721.[MR/doi]
  12. Jennifer R. Daniel and Aloysius G. Helminck, Algorithms for computations in local symmetric spaces, Comm. Algebra 36 (2008), no. 5, 1758–1788.[MR]
  13. Pavel Etingof and Victor Ginzburg, Noncommutative complete intersections and matrix integrals, Pure Appl. Math. Q. 3 (2007), no. 1, part 3, 107–151.[MR/arXiv]
  14. Claus Fieker and Willem A. de Graaf, Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras, LMS J. Comput. Math. 10 (2007), 271–287 (electronic).[MR]
  15. Julia Galstad and Gerald Hoehn, A new class of codes over Z2×Z2, preprint (2010), 29 pages.[arXiv]
  16. University of Georgia VIGRE Algebra Group, On Kostant's theorem for Lie algebra cohomology, Lin, Zongzhu (ed.) et al., Representation Theory. Fourth International Conference on Representation Theory, Lhasa, China, July 16–20, 2007., Contemporary Mathematics, vol. 478, American Mathematical Society (AMS), Providence, RI, 2009, pp. 39–60.
  17. Lothar Gerritzen, Tree polynomials and non-associative Gröbner bases, J. Symbolic Comput. 41 (2006), no. 3-4, 297–316.[MR]
  18. W. A. de Graaf, Using Cartan subalgebras to calculate nilradicals and Levi subalgebras of Lie algebras, J. Pure Appl. Algebra 139 (1999), no. 1–3, 25–39.[MR]
  19. Willem A. de Graaf, Deciding isomorphism of Lie algebras, Proceedings of the Sixth Rhine Workshop on Computer Algebra, Sankt Augustin, March 31 - April 3, 1998, 1998, pp. 9.
  20. Willem A. de Graaf, Lie Algebras: Theory and Algorithms, North-Holland Mathematical Library, vol. 56, North-Holland Publishing Co., Amsterdam, 2000, pp. xii+393.[MR]
  21. Willem A. de Graaf, Classification of solvable Lie algebras, Experiment. Math. 14 (2005), no. 1, 15–25.[MR]
  22. Willem A. de Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra 309 (2007), no. 2, 640–653.[MR]
  23. Jan E. Grabowski, Examples of quantum cluster algebras associated to partial flag varieties, J. Pure Appl. Algebra, to appear (2010), 19 pages.[arXiv]
  24. Jan E. Grabowski and Stéphane Launois, Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: The finite-type cases, Int.Math.Res. Not, to appear (2010), 24 pages.[doi]
  25. Conrad Kobel, On the classification of solvable Lie algebras of finite dimension containing an abelian ideal of codimension one, Master's Thesis, Halmstad University, 2008.
  26. L. G. Kovács and Ralph Stöhr, Lie powers of the natural module for GL(2), J. Algebra 229 (2000), no. 2, 435–462.[MR]
  27. G. I. Lehrer and R. B. Zhang, A Temperley-Lieb analogue for the BMW algebra, preprint (2008), 31 pages.[arXiv]
  28. Sandro Mattarei and Marina Avitabile, Diamonds of finite type in thin Lie algebras, J. Lie Theory 19 (2009), no. 1, 431–439.
  29. Kelly McKinnie, Indecomposable p-algebras and Galois subfields in generic abelian crossed products, J. Algebra 320 (2008), no. 5, 1887–1907.[MR/arXiv]
  30. M. F. Newman and Michael Vaughan-Lee, Engel-4 groups of exponent 5. II. Orders, Proc. London Math. Soc. (3) 79 (1999), no. 2, 283–317.[MR]
  31. Roman O. Popovych, Vyacheslav M. Boyko, Maryna O. Nesterenko, and Maxim W. Lutfullin, Realizations of real low-dimensional Lie algebras, J. Phys. A 36 (2003), 7337-7360.[arXiv]
  32. L. J. Rylands and D. E. Taylor, Constructions for octonion and exceptional Jordan algebras, Des. Codes Cryptogr. 21 (2000), no. 1-3, 191–203.[MR]
  33. S. M. Salamon, Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra 157 (2001), no. 2-3, 311–333.[MR]
  34. Roberto La Scala and Viktor Levandovskyy, Letterplace ideals and non-commutative Gröbner bases, J. Symbolic Comp. 44 (2009), no. 10, 1374-1393.
  35. H. Strade, Lie algebras of small dimension, Lie algebras, vertex operator algebras and their applications, Contemp. Math., vol. 442, Amer. Math. Soc., Providence, RI, 2007, pp. 233–265.[MR]
  36. Donald E. Taylor, Constructing the split octonions, Discovering Mathematics with Magma, Algorithms Comput. Math., vol. 19, Springer, Berlin, 2006, pp. 161–185.[MR]
  37. Michael Vaughan-Lee, Simple Lie algebras of low dimension over GF(2), LMS J. Comput. Math. 9 (2006), 174–192 (electronic).[MR]
  38. Mikael Vejdemo-Johansson, Blackbox computation of A-algebras, Georgian Journal of Mathematics, to appear (2010).[arXiv]
  39. Geordie Williamson, Intersection cohomology complexes on low rank flag varieties, preprint (2007), 17 pages.[arXiv]
  40. Eliana Zoque, A counterexample to the existence of a Poisson structure on a twisted group algebra, preprint (2006), 4 pages.[arXiv]