Proceedings of the Japan Academy, Series A, Mathematical Sciences

A two-parameter quantization of ${GL}\left( n \right)$. (Summary)

Mitsuhiro Takeuchi

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Proc. Japan Acad. Ser. A Math. Sci. Volume 66, Number 5 (1990), 112-114.

First available in Project Euclid: 19 November 2007

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Zentralblatt MATH identifier

Primary: 16W30
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]


Takeuchi, Mitsuhiro. A two-parameter quantization of ${GL}\left( n \right)$. (Summary). Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 5, 112--114. doi:10.3792/pjaa.66.112.

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  • [1] R. Dipper and S. Donkin: Quantum GLn (preprint).
  • [2] L. D. Faddeev, N. Y. Reshetikhin, and L. A. Takhtajan: Quantization of Lie groups and Lie algebras. Algebraic Analysis. Academic Press, pp. 129-140 (1988).
  • [3] M. Hashimoto and T. Hayashi: Quantum multilinear algebra (preprint).
  • [4] G. Lusztig: Quantum deformations of certain simple modules over enveloping algebras. Adv. Math., 70, 237-249 (1988).
  • [5] Y. I. Manin: Quantum groups and non-commutative geometry. CRM Univ. de Montreal (1988).
  • [6] B. Parashall and J.-P. Wang: Quantum linear groups. I, II (preprint).
  • [7] M. Sweedler: Hopf Algebras. W. A. Benjamin, Inc., New York (1969).
  • [8] E. Taft and J. Towber: Quantum deformation of flag schemes and Grassmann schemes. I (preprint).
  • [9] M. Takeuchi: Some topics on GLq(n) (preprint).
  • [10] H. Yamane: A P-B-W theorem for quantized universal enveloping algebra of type AN. Publ. RIMS Kyoto Univ., 25, 503-520 (1989).