Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

Yun Gao

doi:10.1023/A:1001830622499

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An irreducible representation of the extended affine Lie algebra of type $A_{n-1}$ coordinatized by a quantum torus of ν variables is constructed by using the Fock space for the principal vertex operator realization of the affine Lie algebra ${\widetilde{gl}_{n}$.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dokuchaev, M. Figueiredo, L. M. Vasconcellos and Futorny, V. 2003. Imaginary Verma Modules for the Extended Affine Lie Algebrasl2(ℂq). Communications in Algebra, Vol. 31, Issue. 1, p. 289.

Berman, Stephen Gao, Yun and Tan, Shaobin 2003. A unified view of some vertex operator constructions. Israel Journal of Mathematics, Vol. 134, Issue. 1, p. 29.

BILLIG, Y. and ZHAO, K. 2004. VERTEX OPERATOR REPRESENTATIONS OF QUANTUM TORI AT ROOTS OF UNITY. Communications in Contemporary Mathematics, Vol. 06, Issue. 01, p. 195.

Billig, Yuly and Zhao, Kaiming 2004. Weight modules over exp-polynomial Lie algebras. Journal of Pure and Applied Algebra, Vol. 191, Issue. 1-2, p. 23.

Liu, Dong and Hu, Naihong 2004. Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras. Communications in Algebra, Vol. 32, Issue. 6, p. 2385.

Eswara Rao, S. 2004. A class of integrable modules for the core of EALA coordinatized by quantum tori. Journal of Algebra, Vol. 275, Issue. 1, p. 59.

Liu, Dong and Hu, Naihong 2004. Derivation Algebras and 2-Cocycles of the Algebras ofq-Differential Operators. Communications in Algebra, Vol. 32, Issue. 11, p. 4387.

Gao, Yun and Zeng, Ziting 2006. Hermitian representations of the extended affine Lie algebra gl2(Cq)˜. Advances in Mathematics, Vol. 207, Issue. 1, p. 244.

Allison, Bruce Berman, Stephen and Pianzola, Arturo 2006. Iterated loop algebras. Pacific Journal of Mathematics, Vol. 227, Issue. 1, p. 1.

Lin, Weiqiang and Tan, Shaobin 2006. Nonzero level Harish-Chandra modules over the Virasoro-like algebra. Journal of Pure and Applied Algebra, Vol. 204, Issue. 1, p. 90.

Lin, Weiqiang and Tan, Shaobin 2006. Harish-Chandra modules for the q-analog Virasoro-like algebra. Journal of Algebra, Vol. 297, Issue. 1, p. 254.

Wang, Xian-Dong and Zhao, Kaiming 2006. Verma modules over Virasoro-like algebras. Journal of the Australian Mathematical Society, Vol. 80, Issue. 2, p. 179.

Zeng, Ziting 2007. Unitary representations of the extended affine Lie algebra gl3(ℂq). Pacific Journal of Mathematics, Vol. 233, Issue. 2, p. 481.

Lin, Weiqiang and Tan, Shaobin 2008. Graded Modules Over the q-Analog Virasoro-Like Algebra. Algebras and Representation Theory, Vol. 11, Issue. 6, p. 505.

Batra, Punita Guo, Xiangqian Lu, Rencai and Zhao, Kaiming 2009. Highest weight modules over pre-exp-polynomial Lie algebras. Journal of Algebra, Vol. 322, Issue. 12, p. 4163.

Lü, Rencai 2009. Classification of quasifinite modules with nonzero central charges for EALAs of type A with coordinates in quantum torus. Chinese Annals of Mathematics, Series B, Vol. 30, Issue. 2, p. 129.

Lin, Weiqiang and Su, Yucai 2009. Modules for the core of extended affine Lie algebras of typeA1with coordinates in rank 2 quantum tori. Pacific Journal of Mathematics, Vol. 242, Issue. 1, p. 143.

Kong, Xiaoli and Tan, Shaobin 2010. Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra. Communications in Algebra, Vol. 38, Issue. 6, p. 2177.

Wu, Yina and Lin, Weiqiang 2010. Classification of Z-Graded Modules of the Intermediate Series over the q-Analog Virasoro-like Algebra. Algebra Colloquium, Vol. 17, Issue. 02, p. 247.

Zeng, ZiTing 2011. A class of irreducible modules for the extended affine Lie algebra. Science China Mathematics, Vol. 54, Issue. 6, p. 1089.

Download full list

Article contents

Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Representations of Extended Affine Lie Algebras Coordinatized by Certain Quantum Tori

Abstract

Keywords

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests