Quadruples, admissible elements and Herrmann's endomorphisms

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dc.creatorStekolshchik, Rafael
dc.date2006-05-26
dc.date.accessioned2026-07-07T08:49:47Z
dc.date.available2026-07-07T08:49:47Z
dc.descriptionWe 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 $γ_{ij}$. Endomorphism $γ_{ij}$ and the elementary map of Gelfand-Ponomarev $ϕ_i$ act, in a sense, in opposite directions, namely the endomorphism $γ_{ij}$ adds the index to the start of the admissible sequence, and the elementary map $ϕ_i$ adds the index to the end of the admissible sequence.
dc.description44 pages, 7 figures
dc.identifierhttps://arxiv.org/abs/math/0605672
dc.identifierhttp://arxiv.org/abs/math/0605672
dc.identifierJ. Pure Appl. Algebra 211 (2007), no. 1, 95--202
dc.identifierdoi:10.1016/j.jpaa.2007.01.005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144425
dc.subjectRepresentation Theory
dc.subject16G20, 06C05, 06B15
dc.titleQuadruples, admissible elements and Herrmann's endomorphisms
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