Abstract
We construct new integral standard generalized table algebras from parameters of projective geometries. The algebras are noncommutative, imprimitive, and six dimensional.
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Z. Arad, E. Fisman and M. Muzychuk, Generalized table algebras, Israel Journal of Mathematics 114 (1999), 29–60.
T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1986.
A. Hanaki, Clifford theory for association schemes, Journal of Algebra 321 (2009), 1686–1695.
A. Hanaki and M. Hirasaka, Theory of Hecke algebras to association schemes, SUT Journal of Mathematics 38 (2002), 61–66.
A. Hanaki and P.-H. Zieschang, Representation theory of non-commutative association schemes of order 6, Oberwolfach Preprints (2010).
D. G. Higman, Coherent configurations. I. Ordinary representation theory, Geometriae Dedicata 4 (1975), 1–32.
Maxima.sourceforge.net, Maxima, a computer algebra system, version 5.21.1 (2010), http://maxima.sourceforge.net/.
P.-H. Zieschang, An Algebraic Approach to Association Schemes, Lecture Notes in Mathematics, Vol. 1628, Springer-Verlag, Berlin, 1996.
P.-H. Zieschang, Theory of Association Schemes, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005.
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Asaba, Y., Hanaki, A. A construction of integral standard generalized table algebras from parameters of projective geometries. Isr. J. Math. 194, 395–408 (2013). https://doi.org/10.1007/s11856-012-0083-3
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DOI: https://doi.org/10.1007/s11856-012-0083-3