Yuly Billig's Publications

Y. Billig, "Sturm-Liouville problem on Fock space" - PDF

Y. Billig, "Optimal attitude control with two rotation axes" - PDF

Y. Billig, V. Futorny, "Classification of simple cuspidal modules for solenoidal Lie algebras" - to appear in Israel Journal of Mathematics PDF

Y. Billig, V. Futorny, "Classification of simple W_n-modules with finite-dimensional weight spaces" - to appear in Journal fur die reine und angewandte Mathematik (Crelles Journal) PDF

Y. Billig, "Time-optimal decompositions in SU(2)" - Quantum Information Processing, 12 (2013), 955-971. PDF

Y. Billig, J. Dixon "Eigenvalue theorem for systems of polynomial equations" - American Mathematical Monthly, 121 (2014), 150-153. PDF

Y. Billig, "Modules for a sheaf of Lie algebras on loop manifolds" - International Journal of Mathematics, 23 (2012), 1250079 (30 pages). PDF

Y. Billig, V. Futorny "Representations of Lie algebra of vector fields on a torus and chiral de Rham complex" - Transactions of the American Mathematical Society, 366 (2014), 4697-4731. PDF

Y. Billig, M. Lau "Irreducible modules for extended affine Lie algebras", Journal of Algebra, 327 (2011), 208-235. - dvi , PDF or postscript .

Y. Billig, A. Molev, R. Zhang "Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus", Advances in Mathematics, 218, no.6 (2008), 1972-2004. - dvi , PDF or postscript .

Y. Billig, K.-H. Neeb, "On the cohomology of vector fields on parallelizable manifolds", Annales de l'Institut Fourier, 58, no.6 (2008), 1937-1982. - dvi , PDF or postscript .

Y. Billig, M. Lau, "Thin coverings of modules", Journal of Algebra, 316 (2007), 147-173. - dvi , PDF or postscript .

Y. Billig, "Representations of toroidal extended affine Lie algebras", Journal of Algebra, 308 (2007), no. 1, 252-269. - dvi , PDF or postscript .

Y. Billig, "A category of modules for the full toroidal Lie algebra", International Mathematics Research Notices, 2006, Art. ID 68395, 46 pp. - dvi , PDF or postscript .

Y. Billig, V. Futorny, A.Molev, "Verma modules for Yangians," Letters in Mathematical Physics, 78 (2006), no. 1, 1-16. - dvi , PDF or postscript .

Y. Billig, "Jet modules," Canad.J.Math, 59 (2007), no.4, 712-729. - dvi , PDF or postscript .

Y. Billig, "Magnetic hydrodynamics with asymmetric stress tensor," Journal of Mathematical Physics, 46 (2005), no. 4, 043101, 13 pp. - dvi , PDF or postscript .

E.A. Shapiro, M.Yu. Ivanov, Y. Billig, "Coarse-Grained Wavepacket Controllability by Free Evolution and Phase Shifts with Smooth Coordinate Dependance," Journal of Chemical Physics, 120 (2004), 9925-9933. - dvi , PDF or postscipt

Y. Billig, K.Zhao, "Weight modules over exp-polynomial Lie algebras," Journal of Pure and Applied Algebra, 191 (2004), 23-42. - dvi , PDF or postscipt

Y. Billig, "Abelian extensions of the group of diffeomorphisms of a torus," Letters in Mathematical Physics, 64 (2003), 155-169. - dvi , PDF or postscript .

Y. Billig, K.Zhao, "Vertex operator representations of quantum tori at root of unity," Communications in Contemporary Mathematics, 6 (2004), 195-220. - dvi , PDF or postscipt

Y. Billig, "Energy-momentum tensor for the toroidal Lie algebras." - dvi , PDF or postscript .

Y. Billig, "Representations of the twisted Heisenberg-Virasoro algebra at level zero." - Canadian Mathematical Bulletin, 46 (2003), 529-537. - dvi , PDF or postscript .

S.Berman, Y. Billig, J.Szmigielski, "Vertex operator algebras and the representation theory of toroidal algebras" Contemporary Mathematics, 297 (2002), 1-25. - dvi , PDF or postscript .

Y. Billig, "Sine-Gordon equation and representations of affine algebra $\widehat{sl_2}$." Journal of Functional Analysis, 192 (2002), 295-318. - dvi , PDF or postscript .

Y. Billig, A. Pianzola, "Free Kac-Moody groups and their Lie algebras", Algebras and Representation Theory, 5 (2002), 115-136 - dvi , PDF or postscript .

S. Berman, Y. Billig, "Irreducible representations for toroidal Lie algebras" J. Algebra, 221 (1999) 188-231 - dvi , PDF or postscript .

Y. Billig, "An extension of the KdV hierarchy arising from a representation of a toroidal Lie algebra" J. Algebra, 217 (1999) 40-64 - - dvi , PDF or postscript

Y. Billig, "Vertex operator representations for toroidal Lie algebras" J. Math. Phys., 39 (1998), p. 3844-3864 - dvi , PDF or postscript .

Y. Billig, D. Riley, V. Tasic, "Non-matrix varieties and nil-generated algebras whose units satisfy a group identity". J. of Algebra, 190 (1997), p. 241-252 - dvi , PDF or postscript .

Y. Billig, A. Pianzola, "Free groups of Lie type", Comptes Rendus Mathematiques, Royal Soc. of Canada, 18(4) (1996), p. 159-162 - dvi , PDF or postscript .

Y. Billig, "Conjugacy theorem for the strictly hyperbolic Kac-Moody algebras", Communications in Algebra, 23(3) (1995), p.819-840 - dvi , PDF or postscript .

Y. Billig, A. Pianzola, "On Cartan subalgebras", Journal of Algebra, 171(2) (1995), p.397-412.

Y. Billig, A. Pianzola, "Root strings with two consecutive real roots", Tohoku Math. Journal, 47(3) (1995), p.391-403.

Y. Billig, M. Dyer, "Decompositions of Bruhat type for the Kac-Moody groups", Nova Journal for Algebra and Geometry, 3(1) (1994), p.11-40 - dvi , PDF or postscript .

Y. Billig, "On the speciality of Lie algebras with the identities of the algebra $sl_2$, Izvestiya VUZ, 35(10) (1991), 15-18.

Y. Billig, "Affine modular Lie algebras", Matem. Sbornik, 181(8) (1990), 1130-1143.

Y. Billig, "On the homomorphic image of special Lie algebra", Matem. Sbornik, 178(7) (1988), 320-323.

To obtain paper copies of my publications, send e-mail to billig@math.carleton.ca