Preprints, Papers, Books, Lecture notes, Surveys (since 1999)

Preprints

  1. Group schemes over LG-rings and applications to cancellation theorems and Azumaya algebras (with Philippe Gille).

  2. The Norm Functor over Schemes (with Philippe Gille and Cameron Ruether).
    An introduction to norm (= corestriction) over fields and rings, a talk given in the European Non-Associative Algebra Seminar (2024-06-10), Youtube version of my talk

Papers in refereed journals

  1. Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme (with Philippe Gille and Cameron Ruether), previously entitled Quadratic Pairs on Azumaya Algebras over a Scheme. To appear in Trans. Amer. Math. Soc.

  2. Springer's Odd Degree Extension Theorem for Quadratic Forms over semilocal Rings (with Philippe Gille), Indag. Math. (NS) 32 (2021), no. 6, 1290-1310

  3. 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.

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

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

  6. 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

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

  8. 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)

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

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

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

  12. 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.

  13. 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).

  14. Reflection systems and partial root systems (with Ottmar Loos, May 2009, 43 pages), published in Forum Math. 23 (2011), 349–411. This preprint is also available in a previous long version (50 pages). The long version contains more details, but the same results. The

  15. Invertible and nilpotent elements in the group algebra of a unique product group (published in Acta Appl. Math. 108 (2009), 135-139)

  16. Nondegeneracy for Lie triple systems and Kantor pairs (with Esther García and Miguel Gómez Lozana), Canad. Math. Bull. 54(3), 2011, 442-455.

  17. 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.

  18. 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.

  19. 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.

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

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

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

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

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

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

Books

  1. Steinberg Groups for Jordan Pairs, Progress in Mathematics vol. 332, Birkhäuser (hard copy 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)

  2. 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 hard copy, please contact me.

Lecture notes, surveys

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

  2. Steinberg groups for Jordan pairs : an introduction with open problems, 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 vol. 337, Birkhäuser, 77-114.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

Research announcements

  1. 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.

  2. 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.