104
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra

&
Pages 2177-2183 | Received 07 Dec 2008, Published online: 14 Jun 2010

REFERENCES

  • Allison , B. N. , Azam , S. , Berman , S. , Gao , Y. , Pianzola , A. ( 1997 ). Extended affine Lie algebras and their root systems . Mem. Amer. Math. Soc. 126 : 603 .
  • Allison , B. , Gao , Y. ( 2001 ). The root system and the core of an extended affine Lie algebra . Selecta Math. (N. S.) 7 : 149 – 212 .
  • Berman , S. , Gao , Y. , 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. S. , 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 .
  • Berman , S. , Szmigielski , J. ( 1999 ). Principal realization for extended affine Lie algebra of type sl 2 with coordinates in a simple quantum torus with two variables . Contemp. Math. 248 : 39 – 67 .
  • Chari , V. ( 1986 ). Integrable representations of affine Lie algebras . Invent. Math. 85 : 317 – 335 .
  • Chari , V. , Pressley , A. N. ( 1986 ). New unitary representations of loop groups . Math. Ann. 275 : 87 – 104 .
  • Eswara Rao , S. ( 2001 ). Classification of irreducible integrable modules for multi-loop algebras with finite-dimensional weight spaces . J. Algebra 246 : 215 – 225 .
  • Eswara Rao , S. ( 2004 ). Classification of irreducible integrable modules for toroidal Lie algebras with finite dimensional weight spaces . J. Algebra 277 : 318 – 348 .
  • Eswara Rao , S. , Batra , P. ( 2002 ). A new class of representations of EALA coordinated by quantum tori in two variables . Canad. Math. Bull. 45 : 672 – 685 .
  • Gao , Y. ( 2000 ). Representations of extended affine Lie algebras coordinated by certain quantum tori . Compositio Math. 123 : 1 – 25 .
  • Gao , Y. , Zeng , Z. ( 2006 ). Hermitian representations of the extended affine Lie algebra . Adv. Math. 207 : 244 – 265 .
  • Hoegh-Krohn , R. , Torresani , B. ( 1990 ). Classification and construction of quasi-simple Lie algebras . J. Funct. Anal. 89 : 106 – 136 .
  • Jacobson , N. ( 1968 ). Structure and Representations of Jordan Algebras . Amer. Math. Soc. Colloq. Publ. , Vol. 39 , Providence : Amer. Math. Soc. .
  • Mao , X. , Tan , S. ( 2007 ). Vertex operator representations for TKK algebras . J. Algebra 308 : 704 – 733 .
  • Mao , X. , Tan , S. ( 2007 ). Wakimoto representation for the Tits–Kantor–Koecher Lie algebra (in Chinese) . Chinese Ann. Math. 28A : 329 – 338 .
  • Tan , S. ( 1999 ). TKK algebras and vertex operator representations . J. Algebra 211 : 298 – 342 .
  • Yoshii , Y. ( 2000 ). Coordinate algebras of extended affine Lie algebras of type A 1 . J. Algebra 234 : 128 – 168 .
  • Communicated by K. Misra.

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.