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Classification of Quantum Tori with Involution

Published online by Cambridge University Press:  20 November 2018

Yoji Yoshii
Yoji Yoshii*
Affiliation:
Department of Mathematical Sciences University of Alberta Edmonton, Alberta T6G 2G1, email: [email protected]
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Abstract

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Quantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type ${{\text{A}}_{1}}$, $\text{C}$ and $\text{BC}$. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type $\text{C}$.

Keywords

16W50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002 , pp. 711 - 731
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Allison, B., Azam, S., Berman, S., Gao, Y. and Pianzola, A., Extended affine Lie algebras and their root systems. Mem. Amer. Math. Soc. (603) 126, Amer.Math. Soc., Providence, RI, 1997.Google Scholar
[2] Allison, B. and Gao, Y., The root system and the core of an extended affine Lie algebra. Selecta Math. (N.S.) 7 (2001), 1–64.Google Scholar
[3] Allison, B., Benkart, G. and Gao, Y., Lie algebras graded by the root systems BCr, r ≥ 2. To appear.Google Scholar
[4] Azam, S., Nonreduced extended affine root systems of Nullity 3. Comm. Algebra (11) 25 (1997), 3617–3654.Google Scholar
[5] Berman, S., Gao, Y. and Krylyuk, Y., Quantum tori and the structure of elliptic quasi-simple Lie algebras. J. Funct. Anal. 135 (1996), 339–389.Google Scholar
[6] Goodearl, K. R. and Letzter, E. S., Quantum n-space as a quotient of classical n-spaces. Trans. Amer. Math. Soc. (12) 352 (2000), 5855–5876.Google Scholar
[7] Krajewski, T. and Wulkenhaar, R., Perturbative quantum gauge fields on the noncommutative torus. Internat. J. Modern Phys. A (7) 15 (2000), 1011–1029.Google Scholar
[8] McConnell, J. C. and Pettit, J. J., Crossed products and multiplicative analogs of Weyl algebra. J. London Math. Soc. (2) 38 (1988), 47–55.Google Scholar
[9] Parshall, B. and Wang, J.-P., Quantum linear groups. Mem. Amer.Math. Soc. (439) 89, Amer.Math. Soc., Providence, RI, 1991.Google Scholar
[10] Rieffel, M. A., Non-commutative tori.a case study of non-commutative differential manifolds. Contemp.Math. 105 (1990), 191–211.Google Scholar
[11] Yoshii, Y., Coordinate algebras of extended affine Lie algebras of type A1. J. Algebra 234 (2000), 128–168.Google Scholar