47
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Unitary Modules for EALAs Co-ordinatized by a Quantum Torus

Pages 2245-2256 | Received 16 Jan 2002, Published online: 11 Dec 2006

References

  • Allison , B. N. and Gao , Y. 2001 . The root system and the core of an extended affine Lie algebra . Selecta Mathematica New Ser. , 7 : 149 – 212 .
  • Allison , B. N. , Berman , S. , Gao , Y. and Pianzola , A. 1997a . A characterization of affine Kac Moody Lie algebras . Comm. Math. Phys. , 185 : 671 – 688 .
  • Allison , B. N. , Azam , S. , Berman , S. , Gao , Y. and Pianzola , A. 1997b . Extended affine Lie algebras and their root systems . Mem. Amer. Math. Soc. , 126 605
  • Berman , S. and Cox , B. 1994 . Enveloping algebras and representations of toroidal Lie algebras . Pacific J. Math. , 165 : 239 – 267 .
  • Berman , S. and Szmigielski , J. 1999 . Principal realization for extended affine Lie algebra of type sℓ2 with coordinates in a simple quantum torus with two variables . Contemp. Math. , 248 : 39 – 67 .
  • Berman , S. , Gao , Y. and Krylyuk , Y. 1996 . Quantum tori and the structure of elliptic quasi-simple Lie algebras . J. Funct. Anal. , 135 : 339 – 389 .
  • Berman , S. , Gao , Y. , Krylyuk , Y. and Neher , E. 1995 . The alternative torus and the structure of elliptic quasi-simple Lie algebras of type A 2 . Trans. Amer. Math. Soc. , 347 : 4315 – 4363 .
  • Eswara Rao , S. 2001 . “ A class of integrable modules for the core of EALA co-ordinated by Quantum Tori ” . TIFR preprint
  • Eswara Rao , S. and Moody , R. V. 1994 . Vertex representations for n- toroidal Lie algebras and a generalization of the Virasoro algebra . Comm. Math. Phys. , 159 : 239 – 264 .
  • Eswara Rao , S. and Punita Batra . A new class of representations of EALA co-ordinated by Quantum Torus in two variables To appear in Bulletin of the Canadian Mathematical Society (Special volume dedicated to R. V. Moody)
  • Etingof , P. and Frenkel , I. B. 1994 . Central extensions of current groups in two dimensions . Comm. Math. Phys. , 165 : 429 – 444 .
  • Frenkel , I. B. 1985 . “ Representations of Kac-Moody algebras and dual resonance models ” . In Lectures in Appl. Math Vol. 21 , 325 – 353 . Providence : Amer Math. Soc. .
  • Gao , Y. 2000a . Vertex operators arising from the homogeneous realization for . Comm. Math. Phys. , 211 : 745 – 777 .
  • Gao , Y. 2000b . Representations of extended affine Lie-Algebras co-ordinated by certain Quantum Tori. Composita Mathematica . 123 : 1 – 25 .
  • Hoegh-Krohn , R. and Torresani , B. 1990 . Classification and construction of quasi-Simple Lie algebras . J. Funct. Anal. , 89 : 106 – 136 .
  • Kac , V. G. 1990 . “ Infinite dimensional Lie algebras ” . 3rd edn. Cambridge Univ. Press .
  • Kac , V. G. and Raina , A. K. 1987 . “ Highest weight representations of infinite dimensional Lie algebras ” . Singapore : World Scientific .
  • Manin , Y. I. 1991 . “ Topics in Noncommutative Geometry ” . Princeton Univ. Press .
  • Moody , R. V. , Eswara Rao , S. and Yokonuma , I. 1990 . Toroidal Lie algebras and vertex representations . Geom. Dedicata , 35 : 283 – 307 .
  • Wakimoto , M. 1985 . “ Extended affine Lie algebras and a certain series of Hermitian representations ” . Preprint
  • Yamada , H. 1989 . “ Extended affine Lie algebras and their vertex representations ” . Vol. 25 , 587 – 603 . Kyoto U : Publ. RIMS .
  • Yoshii , Y. 1996 . Jordan tori . C.R. Math. Rep. Acad. Sci. Canada , 18 : 153 – 158 .
  • Zhang , H. and Zhao , K. 1996 . Representations of the Virasoro-like Lie algebras and its q-analogue . Comm. Algebra , 24 ( 14 ) : 4361 – 4372 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.