Abstract
This chapter deals with the classification of standard integral GT-algebras (A,B) with L(B) = 1 {1} and |b| ≥ 4 for all b ∈ B# which contain a nonreal faithful basis element b of degree 5. Starting from this point using the basic identity
one can list all possible representations of \( b\bar b \) and b 2 as linear combinations of basis elements (cf. Tables II and III of Subsection 3.3). Assuming that b commutes with \( \bar b \) yields the identity \( \left\langle {b\bar b,b\bar b} \right\rangle = \left\langle {b^2 ,b^2 } \right\rangle \) which reduces the number of these representations (cf. Table III of Subsection 3.3). Then, using various kind of techniques (for example repeated application of the associa- tivity law), each of the reamining cases will be treated separately. In order to state the main result, we introduce the following base of a specific table algebra.
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© 2002 Springer-Verlag Berlin Heidelberg
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Arad, Z., Bünger, F., Fisman, E., Muzychuk, M. (2002). Standard Integral Table Algebras with a Faithful Nonreal Element of Degree 5. 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_3
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DOI: https://doi.org/10.1007/3-540-45558-2_3
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