Fine gradings of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F06%3A04140817" target="_blank" >RIV/68407700:21340/06:04140817 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

čeština

Název v původním jazyce

Fine gradings of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries

Popis výsledku v původním jazyce

Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra $sl(n,\\\\\\\\mathbb{C})$ is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group$Sl(2,\\\\\\\\mathbb{Z}_n)\\\\\\\\times \\\\\\\\mathbb{Z}_2$. In this paper, we deal with a more complicated situation, namely that the fine grading of $sl(p^2, \\\\\\\\mathbb{C})$ is given by a tensor product of the Paulimatrices of the same order $p$, $p$ being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to $Sp(4,\\\\\\\\mathbb{Z}_p)\\\\\\\\times\\

Název v anglickém jazyce

Fine gradings of sl(p2,C) generated by tensor product of generalized Pauli matrices and its symmetries

Popis výsledku anglicky

Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra $sl(n,\\\\\\\\mathbb{C})$ is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group$Sl(2,\\\\\\\\mathbb{Z}_n)\\\\\\\\times \\\\\\\\mathbb{Z}_2$. In this paper, we deal with a more complicated situation, namely that the fine grading of $sl(p^2, \\\\\\\\mathbb{C})$ is given by a tensor product of the Paulimatrices of the same order $p$, $p$ being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to $Sp(4,\\\\\\\\mathbb{Z}_p)\\\\\\\\times\\

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F05%2F0169" target="_blank" >GA201/05/0169: Algebraické a kombinatorické aspekty aperiodických struktur</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2006

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

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Svazek periodika

47

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

013512-013529

Kód UT WoS článku

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EID výsledku v databázi Scopus

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