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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 31, Issue 1

Issues

Normal elements of noncommutative Iwasawa algebras over SL3(ℤ_p)

Dong Han / Feng Wei
  • Corresponding author
  • School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China
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Published Online: 2018-09-10 | DOI: https://doi.org/10.1515/forum-2018-0034

Abstract

Let p be a prime integer and let p be the ring of p-adic integers. By a purely computational approach we prove that each nonzero normal element of a noncommutative Iwasawa algebra over the special linear group SL3(p) is a unit. This gives a positive answer to an open question in [F. Wei and D. Bian, Erratum: Normal elements of completed group algebras over SLn(p) [mr2747414], Internat. J. Algebra Comput. 23 2013, 1, 215] and makes up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over SLn(p), Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously.

Keywords: Iwasawa algebra; normal element

MSC 2010: 11R23; 20C07; 16S34

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About the article


Received: 2018-02-07

Revised: 2018-07-19

Published Online: 2018-09-10

Published in Print: 2019-01-01


Funding Source: Henan Polytechnic University

Award identifier / Grant number: B2010-21

Funding Source: Education Department of Henan Province

Award identifier / Grant number: 16A110031

Award identifier / Grant number: 15A110026

The work of the first author is supported by the Doctor Foundation of Henan Polytechnic University (B2010-21) and the Natural Science Research Program of Education Department of Henan Province (16A110031 and 15A110026).


Citation Information: Forum Mathematicum, Volume 31, Issue 1, Pages 111–147, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2018-0034.

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