Publisher DOI: 10.1007/3-540-45558-2_3
Title: Standard integral table algebras with a faithful nonreal element of degree 5
Language: English
Authors: Ārād, Ṣevî 
Bünger, Florian 
Fisman, E. 
Muzychuk, Mikhail 
Issue Date: 2002
Publisher: Springer
Source: Standard integral table algebras generated by a non-real element of small degree / Zvi Arad; Mikhail Muzychuk (eds.). - Berlin ; Heidelberg [u.a.] : Springer, 2002. - VII, 126 S. ; 24 cm ISBN 3-540-42851-8 kart. : DM 45.90 (Lecture notes in mathematics ; 1773). - Seite 43-81
Part of Series: Lecture notes in mathematics 
Volume number: 1773
Abstract (english): 
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 λxyz|z|⟨xy,z⟩=⟨x,zy¯⟩=λzy¯x|x|,x,y,z∈B, one can list all possible representations of bb¯ and b 2 as linear combinations of basis elements (cf. Tables II and III of Subsection 3.3). Assuming that b commutes with b¯ yields the identity ⟨bb¯,bb¯⟩=⟨b2,b2⟩ 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. © Springer-Verlag Berlin Heidelberg 2002
URI: http://hdl.handle.net/11420/9429
ISBN: 978-3-540-42851-0
3-540-42851-8
Institute: Zuverlässiges Rechnen E-19 
Document Type: Chapter (Book)
Appears in Collections:Publications without fulltext

Show full item record

Page view(s)

8
checked on May 6, 2021

Google ScholarTM

Check

Add Files to Item

Note about this record

Cite this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.