Research Article
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Year 2020, Volume 28, Issue 28, 175 - 186, 14.07.2020
https://doi.org/10.24330/ieja.768246

Abstract

References

  • M. Chlebowitz and B. Külshammer, Symmetric local algebras with 5-dimensional center, Trans. Amer. Math. Soc., 329(2) (1992), 715-731.
  • T. C. Craven and T. L. Smith, Symmetric algebras over rings and fields, Bull. Aust. Math. Soc., 89(3) (2014), 466-472.
  • C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, preprint, arXiv:1612.03485v4, (2019).
  • R. Kessar, On blocks stably equivalent to a quantum complete intersection of dimension 9 in characteristic 3 and a case of the Abelian Defect Group Conjecture, J. Lond. Math. Soc., 85(2) (2012), 491-510.
  • B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88 (1984), 190-195.
  • P. Landrock, Eine Klasse von Blocken mit Einer Elementarabelschen Defektgruppe der Ordnung 16, Ph.D. Thesis, Jena 2018.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.

ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS

Year 2020, Volume 28, Issue 28, 175 - 186, 14.07.2020
https://doi.org/10.24330/ieja.768246

Abstract

This article is motivated by some results from Chlebowitz and Külshammer on how the structure of a symmetric local algebra is influenced by its center. They have shown that a symmetric local algebra is almost always commutative if its center is at most 5-dimensional. In this article we are interested in how the ideal property of the radical of the center of a symmetric local algebra is influenced by the dimension of the algebra itself. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • M. Chlebowitz and B. Külshammer, Symmetric local algebras with 5-dimensional center, Trans. Amer. Math. Soc., 329(2) (1992), 715-731.
  • T. C. Craven and T. L. Smith, Symmetric algebras over rings and fields, Bull. Aust. Math. Soc., 89(3) (2014), 466-472.
  • C. W. Eaton, Morita equivalence classes of blocks with elementary abelian defect groups of order 16, preprint, arXiv:1612.03485v4, (2019).
  • R. Kessar, On blocks stably equivalent to a quantum complete intersection of dimension 9 in characteristic 3 and a case of the Abelian Defect Group Conjecture, J. Lond. Math. Soc., 85(2) (2012), 491-510.
  • B. Külshammer, Symmetric local algebras and small blocks of finite groups, J. Algebra, 88 (1984), 190-195.
  • P. Landrock, Eine Klasse von Blocken mit Einer Elementarabelschen Defektgruppe der Ordnung 16, Ph.D. Thesis, Jena 2018.
  • P. Landrock and B. Sambale, On centers of blocks with one simple module, J. Algebra, 472 (2017), 339-368.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Pierre LANDROCK This is me (Primary Author)
University of Jena
Germany

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768246, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {175 - 186}, doi = {10.24330/ieja.768246}, title = {ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS}, key = {cite}, author = {Landrock, Pierre} }
APA Landrock, P. (2020). ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS . International Electronic Journal of Algebra , 28 (28) , 175-186 . DOI: 10.24330/ieja.768246
MLA Landrock, P. "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS" . International Electronic Journal of Algebra 28 (2020 ): 175-186 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768246>
Chicago Landrock, P. "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS". International Electronic Journal of Algebra 28 (2020 ): 175-186
RIS TY - JOUR T1 - ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS AU - PierreLandrock Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768246 DO - 10.24330/ieja.768246 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 175 EP - 186 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768246 UR - https://doi.org/10.24330/ieja.768246 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS %A Pierre Landrock %T ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768246 %U 10.24330/ieja.768246
ISNAD Landrock, Pierre . "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS". International Electronic Journal of Algebra 28 / 28 (July 2020): 175-186 . https://doi.org/10.24330/ieja.768246
AMA Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. IEJA. 2020; 28(28): 175-186.
Vancouver Landrock P. ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS. International Electronic Journal of Algebra. 2020; 28(28): 175-186.
IEEE P. Landrock , "ON THE RADICAL OF THE CENTER OF SMALL SYMMETRIC LOCAL ALGEBRAS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 175-186, Jul. 2020, doi:10.24330/ieja.768246