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

Result code in 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>

Result on the web

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DOI - Digital Object Identifier

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Result language

čeština

Original language name

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

Original language description

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\\

Czech name

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

Czech description

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\\

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F05%2F0169" target="_blank" >GA201/05/0169: Algebraic and combinatorial aspects of aperiodic structures</a><br>

Continuities

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

Publication year

2006

Confidentiality

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

Name of the periodical

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

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Volume of the periodical

47

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

18

Pages from-to

013512-013529

UT code for WoS article

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EID of the result in the Scopus database

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