Abstract
Let R be an integral domain. An R-algebra A with a distinguished basis B is called a generalized table algebra (briefly, GT-algebra) with a distinguished basis B if it satisfies the following axioms:
GT0. A is a free left R-module with a basis B.
GT1. A is an R-algebra with unit 1, and 1 ∈ B.
GT2. There exists an antiautomorphism a → ā, a ∈ A, such that \( \overline {(\bar a)} \) = a holds for all a ∈ A and \( \overline B \) = B.
Let λ λabc ∈ R be the structure constants of A in the basis B, i.e., {E1-1}
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© 2002 Springer-Verlag Berlin Heidelberg
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Arad, Z., Muzychuk, M. (2002). Introduction. In: Arad, Z., Muzychuk, M. (eds) Standard Integral Table Algebras Generated by Non-real Element of Small Degree. Lecture Notes in Mathematics, vol 1773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45558-2_1
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DOI: https://doi.org/10.1007/3-540-45558-2_1
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