Algebras – Associative

  1. Noah Arbesfeld and David Jordan, New results on the lower central series quotients of a free associative algebra, J. Algebra 323 (2010), no. 6, 1813–1825.[MR/doi]
  2. Martina Balagovic and Anirudha Balasubramanian, On the lower central series quotients of a graded associative algebra, J. Algebra, to appear (2010).[arXiv]
  3. Werner Bley and Henri Johnston, Computing generators of free modules over orders in group algebras, J. Algebra 320 (2008), no. 2, 836–852.[MR]
  4. Werner Bley and Stephen M. J. Wilson, Computations in relative algebraic K-groups, LMS J. Comput. Math. 12 (2009), 166–194.[MR/doi]
  5. N. Bourbaki, Algèbres tensorielles, algèbres extérieures, algèbres symétriques, Algèbre, Bourbaki, Springer, 2007, pp. 379–596.
  6. Jon F. Carlson and Graham Matthews, Generators and relations for matrix algebras, J. Algebra 300 (2006), no. 1, 134–159.[MR]
  7. Alexander Chistov, Gábor Ivanyos, and Marek Karpinski, Polynomial time algorithms for modules over finite dimensional algebras, in Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), ACM, New York, 1997, pp. 68–74 (electronic).[MR]
  8. Robert S. Coulter, George Havas, and Marie Henderson, Giesbrecht's algorithm, the HFE cryptosystem and Ore's ps-polynomials, Computer Mathematics (Matsuyama, 2001), Lecture Notes Ser. Comput, vol. 9, World Sci. Publ., River Edge, NJ, 2001, pp. 36–45.[MR]
  9. Galyna Dobrovolska and Pavel Etingof, An upper bound for the lower central series quotients of a free associative algebra, Int. Math. Res. Not. IMRN (2008), no. 12, Art. ID rnn039, 10.[MR]
  10. Galyna Dobrovolska, John Kim, and Xiaoguang Ma, On the lower central series of an associative algebra (with an appendix by Pavel Etingof), J. Algebra 320 (2008), no. 1, 213–237.[MR]
  11. 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]
  12. Pavel Etingof, John Kim, and Xiaoguang Ma, On universal Lie nilpotent associative algebras, J. Algebra 321 (2009), no. 2, 697–703.[MR/doi]
  13. Pavel Etingof, Alexei Oblomkov, and Eric Rains, Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces, Adv. Math. 212 (2007), no. 2, 749–796.[MR]
  14. Ching-Hwa Eu and Travis Schedler, Calabi-Yau Frobenius algebras, J. Alg. 321 (2009), no. 3, 774-815.[arXiv]
  15. Boris Feigin and Boris Shoikhet, On [A,A]/[A, [A,A]] and on a Wn-action on the consecutive commutators of free associative algebra, Math. Res. Lett. 14 (2007), no. 5, 781–795.[MR/arXiv]
  16. Victor Ginzburg, Calabi-Yau algebras, preprint (2007), 79 pages.[arXiv]
  17. David J. Green, Gröbner bases for p-group algebras, preprint (2009).[arXiv]
  18. Edward L. Green, Lenwood S. Heath, and Craig A. Struble, Constructing endomorphism rings via duals, in ISSAC '00: Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), ACM, New York, 2000, pp. 129–136 (electronic).[MR]
  19. Edward L. Green, Lenwood S. Heath, and Craig A. Struble, Constructing homomorphism spaces and endomorphism rings, J. Symbolic Comput. 32 (2001), no. 1-2, 101–117.[MR/link]
  20. Edward L. Green and Øyvind Solberg, An algorithmic approach to resolutions, J. Symbolic Comput. 42 (2007), no. 11-12, 1012–1033.[MR]
  21. Robert Guralnick and Susan Montgomery, Frobenius-Schur indicators for subgroups and the Drinfeld double of Weyl groups, Trans. Amer. Math. Soc. 361 (2009), no. 7, 3611–3632.[MR/arXiv]
  22. Emmanuel Hallouin and Christian Maire, Cancellation in totally definite quaternion algebras, J. Reine Angew. Math. 595 (2006), 189–213.[MR]
  23. Timo Hanke, A twisted Laurent series ring that is a noncrossed product, Israel J. Math. 150 (2005), 199–203.[MR]
  24. Timo Hanke, The isomorphism problem for cyclic algebras and an application, ISSAC 2007, ACM, New York, 2007, pp. 181–186.[MR/arXiv]
  25. Miles Lee Holloway, Derived equivalences for group algebras, PhD Thesis, University of Bristol, 2001.
  26. Gábor Ivanyos and Klaus Lux, Treating the exceptional cases of the MeatAxe, Experiment. Math. 9 (2000), no. 3, 373–381.[MR]
  27. Brent Kerby, Automorphism groups of Schur rings, preprint (2009), 21 pages.[arXiv]
  28. Markus Kirschmer and John Voight, Algorithmic enumeration of ideal classes for quaternion orders, SIAM J. Comput 39 (2010), no. 5, 1714–1747.
  29. Max-Albert Knus and Jean-Pierre Tignol, Triality and etale algebras, Quadratic Forms, Linear Algebraic Groups, and Cohomology, Developments in Mathematics, vol. 18, Springer New York, 2010, pp. 259–286.[doi]
  30. R. V. Kravchenko and B. V. Petrenko, Some formulas for the minimal number of generators of the direct sum of matrix rings, preprint (2007), 23 pages.[arXiv]
  31. Matthias Künzer, On representations of twisted group rings, J. Group Theory 7 (2004), no. 2, 197–229.[MR/link]
  32. Sefi Ladkani, On the periodicity of Coxeter transformations and the non-negativity of their Euler forms, Linear Algebra Appl. 428 (2008), no. 4, 742–753.[MR]
  33. Klaus M. Lux and Magdolna Szőke, Computing homomorphism spaces between modules over finite dimensional algebras, Experiment. Math. 12 (2003), no. 1, 91–98.[MR]
  34. Klaus M. Lux and Magdolna Szőke, Computing decompositions of modules over finite-dimensional algebras, Experiment. Math. 16 (2007), no. 1, 1–6.[MR]
  35. Graham Matthews, Computing Generators and Relations for Matrix Algebras, PhD Thesis, University of Georgia, 2004.
  36. Gabriele Nebe and Allan Steel, Recognition of division algebras, J. Algebra 322 (2009), no. 3, 903–909.[doi]
  37. Jana Pílniková, Trivializing a central simple algebra of degree 4 over the rational numbers, J. Symbolic Comput. 42 (2007), no. 6, 579–586.[MR]
  38. M. Anwar Rao and Robert Sandling, The characterisation of modular group algebras having unit groups of nilpotency class 3, Canad. Math. Bull. 38 (1995), no. 1, 112–116.[MR]
  39. I. K. Redchuk, Finite-dimensionality and growth of algebras defined by polylinearly connected generators, Ukraïn. Mat. Zh. 57 (2005), no. 10, 1435–1440.[MR]
  40. Robert Sandling, Presentations for unit groups of modular group algebras of groups of order 16, Math. Comp. 59 (1992), no. 200, 689–701.[MR]
  41. Bernd Souvignier, Decomposing homogeneous modules of finite groups in characteristic zero, J. Algebra 322 (2009), no. 3, 948–956.
  42. Craig A. Struble, Analysis and implementation of algorithms for noncommutative algebra, PhD Thesis, Virginia Polytechnic Institute and State University, 2000.[link]
  43. Yi Sun, Finite dimensional representations of the rational Cherednik algebra for G4, J. Algebra 323 (2010), no. 10, 2864–2887.[MR/doi]
  44. John Voight, Quadratic Forms and Quaternion Algebras: Algorithms and Arithmetic, PhD Thesis, Berkeley, 2005.
  45. John Voight, Identifying the matrix ring: Algorithms for quaternion algebras and quadratic forms, preprint (2010), 35 pages.[arXiv]
  46. Katsushi Waki, Calculation of direct summands of FG-modules, Sci. Rep. Hirosaki Univ. 44 (1997), no. 2, 193–200.[MR]
  47. Stewart Wilcox, Complementation in the group of units of matrix rings, Bull. Austral. Math. Soc. 70 (2004), no. 2, 223–227.[MR]
  48. Eliana Zoque, A counterexample to the existence of a Poisson structure on a twisted group algebra, preprint (2006), 4 pages.[arXiv]