Proceedings of the Japan Academy, Series A, Mathematical Sciences

A uniform construction of the root lattices $E_6, E_7, E_8$ and their dual lattices

Tetsuji Shioda

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 71, Number 7 (1995), 140-143.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195510601

Digital Object Identifier
doi:10.3792/pjaa.71.140

Mathematical Reviews number (MathSciNet)
MR1363900

Zentralblatt MATH identifier
0854.17008

Subjects
Primary: 17B20: Simple, semisimple, reductive (super)algebras

Citation

Shioda, Tetsuji. A uniform construction of the root lattices $E_6, E_7, E_8$ and their dual lattices. Proc. Japan Acad. Ser. A Math. Sci. 71 (1995), no. 7, 140--143. doi:10.3792/pjaa.71.140. https://projecteuclid.org/euclid.pja/1195510601


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References

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  • [2] Conway, J. and Sloane, N.: Sphere Packings, Lattices and Groups. Springer-Verlag (1988); 2nd ed. (1993).
  • [3] Manin, Yu.: Cubic Forms. North-Holland (1974); 2nd ed. (1986).
  • [4] Shioda, T.: Construction of elliptic curves with high rank via the invariants of the Weyl groups. J. Math. Soc. Japan, 43, 673-719 (1991).
  • [5] Shioda, T.; Theory of Mordell-Weil lattices. Proc. ICM Kyoto, 1990, Springer, vol. I, pp. 473-489 (1991).
  • [6] Shioda, T.: Plane quartics and Mordell-Weil lattices of type E7. Comment. Math. Univ. St. Pauli, 42, 61-79 (1993).
  • [7] Shioda, T.: Weierstrass transformations and cubic surfaces. Comment. Math. Univ. St. Pauli, 44, 109-128 (1995).