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Quadruples, admissible elements and Herrmann's endomorphisms | | Rafael Stekolshchik
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26 May 2006 | | Subject: | Representation Theory | | Abstract: | We obtain a connection between admissible elements for quadruples and Herrmann’s endomorphisms. Herrmann constructed perfect elements $s_n$, $t_n$, $p_{i,n}$ in $D^4$ by means of some endomorphisms and showed that these perfect elements coincide with the Gelfand-Ponomarev perfect elements modulo linear equivalence. We show that the admissible elements in $D^4$ are also obtained by means of Herrmann’s endomorphisms $gamma_{ij}$. Endomorphism $gamma_{ij}$ and the elementary map of Gelfand-Ponomarev $phi_i$ act, in a sense, in opposite directions, namely the endomorphism $gamma_{ij}$ adds the index to the start of the admissible sequence, and the elementary map $phi_i$ adds the index to the end of the admissible sequence. | | Source: | arXiv, math/0605672 | | Services: | Forum | Review | PDF | Favorites | |
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