Preprints and Papers (since 1999)

(All preprints are in pdf format)
  1. Springer's Odd Degree Extension Theorem for Quadratic Forms over semilocal Rings (with Philippe Gille), to appear in Indag. Math.

  2. Steinberg Groups for Jordan Pairs, Progress in Mathematics vol. 332, Birkhäuser (pdf version available, please send me an email)

    (Talk on Steinberg Groups for Jordan pairs at the workshop Nonassociative Algebras and Geometry, August 2019, Bonne Bay Marine Station, Newfoundland)

  3. Steinberg groups for Jordan pairs - an introduction with open problems, to appear in Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification: In Honor of Vyjayanthi Chari on the Occasion of her 60th Birthday', Progress in Mathematics, Birkhäuser.

  4. Conjugacy of Cartan subalgebras in EALAs with a non-fgc centreless core (with Vladimir Chernousov and Arturo Pianzola); Trans. Moscow Math. Soc. 78 (2017, Vinberg's volume) , 235-256.

  5. Integrable representations of root-graded Lie algebras (with Nathan Manning and Hadi Salmasian); Journal of Algebra 500 (2018), 253-302.

  6. On conjugacy of Cartan subalgebras in non-fgc Lie tori (with Vladimir Chernousov and Arturo Pianzola); Transformation Groups 21 (2016), 1003-1037.

  7. On conjugacy of Cartan subalgebras in extended affine Lie algebras (with Vladimir Chernousov, Arturo Pianzola, and Uladzimir Yahorau); Advances in Mathematics 290 (2016), 260-292

  8. Extensions and block decompositions for finite-dimensional representations of equivariant map algebras (with Alistair Savage, Transformation Groups 20 (2015), 183-228)

  9. Invariant bilinear forms of algebras given by faithfully flat descent (with Arturo Pianzola, Daniel Prelat and Claudia Sepp), Communications in Contemporary Mathematics 17 (2015), 1450009 (37 pages), DOI: 10.1142/S0219199714500096 (Talk at the CMS winter meeting 2013, Ottawa)

  10. Étale Descent of Derivations (with Arturo Pianzola), Transformation Groups 18 (2013), 1189-1205.

  11. A survey of equivariant map algebras with open problems (with Alistair Savage, Contemporary Mathematics vol. 602 (2013), 165-182)

  12. Universal central extensions of direct limits of Lie superalgebras (with Jie Sun), Journal of Algebra 368 (2012), 169-181.

  13. Basic polynomial invariants, fundamental representations and the Chern class map (with Sanghoon Baek and Kirill Zainoulline), Documenta Math. 17 (2012), 135-150.

  14. Lie tori of type B_2 and graded-simple Jordan structures covered by a triangle (with Maribel Tocón), Journal of Algebra 344 (2011), 78-113, contains the proofs of the research announcement Graded-simple Lie algebras of type B_2 and Jordan systems covered by a triangle, posted below.

  15. Irreducible finite-dimensional representations of equivariant map algebras (with Alistair Savage and Prasad Senesi), Trans. Amer. Math. Soc. 364 (2012), 2619-2646 ( talk) at the CMS Winter meeting 2009, Windsor.

  16. Lectures on extended affine Lie algebras, given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras, Ottawa June 2009. Published as Extended affine Lie algebras -- an introduction to their structure theory, pages 107-167 of a Fields Institute Communications series volume on Geometric Representation Theory and Extended Affine Lie Algebras, edited by E. Neher, A. Savage and W. Wang.

  17. Reflection systems and partial root systems (with Ottmar Loos, May 2009, 43 pages), published in Forum Math. 23 (2011), 349411. This preprint is also available in a previous long version (50 pages). The long version contains more details, but the same results. The additional text is marked in the form >> ...(additional text)...<<.
    Abstract: We develop a general theory of reflection systems and, more specifically, partial root systems which provide a unifying framework for finite root systems, Kac-Moody root systems, extended affine root systems and various generalizations thereof. Nilpotent and prenilpotent subsets are studied in this setting, based on commutator sets and the descending central series. We show that our notion of a prenilpotent pair coincides, for Kac-Moody root systems, with the one defined by Tits in terms of positive systems and the Weyl group.

  18. Invertible and nilpotent elements in the group algebra of a unique product group (published in Acta Appl. Math. 108 (2009), 135-139)
    Abstract: We describe the nilpotent and invertible elements in group algebras k[G] for k a commutative associative unital ring and G a unique product group, for example an ordered group.

  19. Extended affine Lie algebras and other generalizations of affine Lie algebras -- a survey (June 2008) This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras. It appeared in Developments and trends in infinite-dimensional Lie theory, 53-126, Progr. Math., 288, Birkhäuser Boston, Inc., Boston, MA, 2011, editors: K.-H. Neeb and A. Pianzola.

  20. Nondegeneracy for Lie triple systems and Kantor pairs (with Esther García and Miguel Gómez Lozana), Canad. Math. Bull. 54(3), 2011, 442-455.
    Abstract: We study the transfer of nondegeneracy between Lie triple systems and their standard Lie algebra envelopes as well as between Kantor pairs, their associated Lie triple systems and their Lie algebra envelopes. We also show that simple Kantor pairs and Lie triple systems in characteristic 0 are nondegenerate.

  21. Graded-simple Lie algebras of type B_2 and Jordan systems covered by a triangle (with Maribel Tocón, preprint March 2007). This is a research announcement which appeared in the proceedings of the satellite conference of the ICM 2006 ``From Lie Algebras to Quantum Groups", held at the University of Coimbra (Portugal), June 28-30, 2006.
    Abstract: We announce a classification of graded-simple Jordan systems covered by a compatible triangle, under some natural assumptions on the abelian group, in order to get the corresponding classification of graded-simple Lie algebras of type B2.

  22. An introduction to the theory of extended affine Lie algebras , based on a lecture at the Oberwolfach meeting on "Infinite dimensional Lie Theory", Dec. 10-16, 2006. Appeared in Oberwolfach Reports.

  23. A construction of gradings of Lie algebras (with Antonio Fernández López, Esther García and Miguel Gómez Lozano); Int. Math. Res. Not. IMRN, 2007, no. 16, Art. ID rnm051, 34 pages; the published version has some strange formatting.
    Abstract: In this paper we present a method to construct gradings of Lie algebras. It requires the existence of an abelian inner ideal B of the Lie algebra whose subquotient, a Jordan pair, is covered by a finite grid, and it produces a grading of the Lie algebra L by the weight lattice of the root system associated to the covering grid. As a corollary one obtains a finite Z-grading of L in the form L=L_{-n} + ... + L_n such that B=L_n. In particular, our assumption on B holds for abelian inner ideals of finite length in nondegenerate Lie algebras.

  24. The centroid of extended affine and root graded Lie algebras (with Georgia Benkart, Journal of Pure and Applied Algebra, vol. 205 (2006), no.1, 117--154.
    Abstract: We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.

  25. Extended affine Lie Algebras (August 2004, 11 pages)
    This is a research announcement. A shortened version has been published in two parts in the Mathematical Reports of the Academy of Science of the Royal Society of Canada:
    Lie Tori, C. R. Math. Rep. Acad. Sci. Canada Vol. 26, (3), 2004 pp. 84-89 and
    Extended affine Lie algebras, C. R. Math. Rep. Acad. Sci. Canada Vol. 26, (3), 2004 pp. 90-96.

  26. Locally finite root systems (with Ottmar Loos), published as Memoirs of the Amer. Math. Soc. vol. 171, number 811 (2004). If you would like a paper copy please contact me.

  27. Gelfand-Kirillov dimension and local finiteness of Jordan superpairs covered by grids and their associated Lie superalgebras (with Esther García, Feb. 2002, 25 pages). Published in Communications in Algebra, 32 (2004), 2149--2176.

  28. Semiprime, prime and simple Jordan superpairs covered by grids, (with Esther García), Journal of Algebra 273 (2004), 1--32.

  29. Tits-Kantor-Koecher Superalgebras of Jordan superpairs covered by grids (with Esther García, 2001). Communications in Algebra, 31 (2003), no. 7, 3335--3375.

  30. Quadratic Jordan superpairs covered by grids Journal of Algebra, 269 (2003), 28-73.

  31. An introduction to universal central extensions of Lie superalgebras (July 2002, 19 pages) A re-formatted version has appeared in the conference proceedings of Groups, rings, Lie and Hopf algebras (St. John's, NF, 2001, 141--166, (St. John's, NF, 2001), Math. Appl., 555, Kluwer Acad, Publ, Dordrecht, 2003.

  32. Derivations and invariant forms of Jordan and alternative tori (with Yoji Yoshii). Published in Trans. Amer. Math. Soc. 33 (2003), 1079--1108.

  33. Transformation groups of the Andersson-Perlman cone, Journal of Lie Theory, 9 (1999), no. 1, 203--213.

  34. Polynomial Identities and non-identities of split Jordan pairs, Journal of Algebra, 211 (1999), no. 1, 206--224.